We often hear these accusations of faith-based science. But it is far from clear what the accusers mean by faith.
This will be a somewhat lengthy response, as I go through examples from my own experience. You can decide whether or not they depend on faith. And, when you have decided that, let us know so that we can try to work out what you mean by "faith".
Example 1 - from personal life
My wife takes the commuter train into Chicago on work days. The inbound train usually stops at the north platform. But, occasionally, it is on a different track so one must board from the south platform. There is usually a loud speaker announcement when boarding will be from the south platform.
Issue 1: Is it faith to believe what the loudspeaker announcement says?
In practice, I usually drive my wife to the station. If we see that most of the people are at the south platform, I will drop her off there. Otherwise, I will drop her off at the north platform.
Issue 2: Is it faith to go by what other people are doing?
There are some other alternatives here. We can look at the signal lights on the track. And if the signals on the north track are set for an outbound train (a train going in the wrong direction), then the inbound train will probably be on the south track. But this is not 100% reliable - signals have been known to be switched at the last moment
The most reliable method is to wait at the crossing point until the train is in sight. Then, decide which platform to wait on, after seeing which track the train is on. But there's a problem here, too. By the time that the train is close enough to tell which track it is on, there is very little time to cross before the gates lower and bar crossing to the other side.
Commentary: Philosophers say that knowledge is justified true belief. But what the train example illustrates, is that we often have to manage without certainty. We can get by with weak justification for weakly held beliefs. And I think that is a big difference with religion. For religion insists on certainty, whereas science admits that scientific knowledge is tentative and subject to revision when there is new evidence.
Example 2 - from mathematics
I'm a mathematician. I actually have a paper published in number theory. There's a famous example in number theory, known as Fermat's Last Theorem, which Fermat claimed to have proved but he did not leave us a proof. Almost nobody believes that Fermat actually had a proof. More recently, the theorem has been proved by Andrew Wiles. The proof is long and difficult. I have not actually read the proof, but I do believe the result.
Issue 3: Am I relying of faith, in believing Fermat's last theorem?
My take is this: Some good mathematicians have checked Wiles' proof. I take that as sufficient evidence to support my belief. However, if I wanted to prove something else that depended on FLT, then I would feel obliged to read and understand Wiles' proof first.
That Wiles' proof has been checked by others is sufficient evidence for an ordinary belief in the truth of FLT. But it is not strong enough for the kind of certainty that I would need in order to build on top of that result.
Example 3 - biology
I am not a biologist. I did take one year of biology in my freshman year as an undergraduate, and did learn about evolution there, though I had heard of it previously.
The evidence for evolution can, at most, be indirect evidence for me. I have not done the field work. I have to rely on the reports by paleontologists, biochemists, etc.
I'll start with the theory of evolution. My general take on scientific theories, is that they are neither true nor false. The define a methodology to use in the field, and they define the terminology. We accept theories because they work well. That is to say, scientific theories are pragmatic constructs.
Let's look at some examples of what could be considered theories:
Kepler's laws of planetary motion - false, well known to be false, but a very useful approximation;
The gas laws (Boyle's law, for example) - false, well known to be false, but a very useful approximation;
Newton's laws of motion - true by definition of the terms involved, so they are unfalsifiable. But they are very useful because they allowed us to vastly extend what we could measure and to vastly increase the amount of information that we could thereby obtain.
Note that some people will disagree with my view of those laws, particularly with my view of Newton's laws.
The point here is that we value scientific theories for their usefulness, not for their truth. Both Kepler's laws and the gas laws are idealizations. Every physicist knows that reality does not match the ideal. But the idealization is useful as a starting point.
Back to evolution. I see the theory of evolution as, likewise, being an idealization. Strictly speaking, it is not true. Horizontal gene transfer is observed, but is not strictly according to the theory. One of the annoying things about creationists, is that they somehow think that they can disprove the theory of evolution with a counter example, and thereby throw out all of evolutionary theory. But we don't expect the theory to be literally true. We take it to be an idealization, much as we do with other scientific theories. If creationists want to see evolution tossed out, then they will need to come up with something that is at least as useful.
While strictly speaking, the theory is an idealization, it does tell us a lot about the biosphere. When I am solving a jigsaw puzzle, I do not have a logical proof that I have everything right. Rather, the pieces all fit together so well, that it is inconceivable that my solution to the jigsaw puzzle is not mostly correct. It is the same with evolution. The pieces all fit together so well, in the picture they give us of the biosphere, that it is inconceivable that it is not mostly right.
Issue 4: Does that amount to accepting evolution on faith? Does it involve faith to accept that a jigsaw puzzle is solved?
You specifically asked about origins questions. So let me address two of those:
(a) the origin of life: I do not know how life originated. I suspect that we will never have enough data to be certain about that. I believe that life mostly likely originated by natural means. I'm inclined to the view that "metabolism first" is more likely than "replicator first". But I cannot prove that. My position is tentative.
I have not ruled out that life began in an magical ("poofing into existence") act of divine creation. But I think that unlikely. All of the evidence we have suggests that if there is/was a divine creator, then that creator has always used natural means of carrying out the creation. So the best evidence suggests a natural origin of life, even if a creator was involved.
(b) the origin of species. The theory of evolution gives a good account of processes that are at work, and that could have resulted in the biological diversity that we see. However, for most species we do not have direct evidence. It is conceivable that one or more species were created by magical poofing into existence. It is conceivable, but it is highly implausible. And as more evidence of our presumed hominid ancestors shows up, it becomes more and more implausible that homo sapiens arose by means other than natural processes. And those natural processes are what the theory of evolution idealizes. It is likely that there was some horizontal gene transfer involved. It is likely that something similar to the endosymbiosis (proposed by Lynn Margulis) was involved. So I don't assume evolution occurred strictly in accordance with the idealized theory. However, evolution of some not-so-idealized type seems to be the explanation.
Issue 5: Does it follow that I take evolution on faith?
What we see with creationists is certainty about their creationist beliefs, in spite of considerable evidence to the contrary. And that's about what I take "faith" to mean.
By contrast, with scientists we see tentativity about their beliefs, even though those beliefs are strongly supported by evidence. I don't see that as at all similar to faith.
Fundamentalism - the anti-American, anti-Christian branch of American Christianity