Problems with the first life

Alright lets pretend that somehow a cell was formed in a primative ocean. Lets say that this cell somehow because of "chemicals" has all the necessary organelles(and the chances of this happening are.......). The first life you think would be pretty fragile, yet because there had to have been no oxygen in the atmosphere there obviously would NOT be an ozone layer. Without an ozone layer this cell would receive heavy doses radiation from the sun- obviously this would kill it.Lets say that it magically survives and somehow this cell mutated so that it magically mastered many essential life process-for example-Protein Synthesis- It had to have a mutation that would create mRNA and somehow a mutation to get it to the right place and somehow another mutation for the tRNA to develope and so on. If one of these "mutations" that created the process of protein synthesis was wrong- lets say the tRNA was brought to the vacuole- the cell DOES NOT survive.Somehow this cell also had a mutation that caused it to be able to reproduce asexually- if it didn't have this mutation- we wouldn't be here right now.Lets say that chemicals in this primitive ocean make millions and millions of cells complete with all organelles- NOT from asexual reproduction but because of some kinda chemical reaction.
How likely is it that one of these cells is going to have a mutation for the process of protein synthesis? A mutation that would create anything beneficial to the cell? If any of these cells had a mutation they would probably die.

"You answered this in the first part of your paragraph - the ocean protects it, if it's deep enough.""Dosing of the first cell or pre-cells with radiation would have increased mutation/breakage/rearrangement rate in the nucleic acids of those cells, thus potentially accelerating evolution."pink sasquatch, you and crashfrog have different arguments

" Out of the millions or billions of planets capable of sustaining life we just happen to be on Earth. "How exactly do you know that there are millions and billions of planets that can sustain life?'We could be the only planet in the solar system with life or we could be 1 of millions and millions of planets with life. We just don't know, so really cannot make say something like that.