Is atheism a scientific perspective?

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Evolution relies on chance events from the remote past.

Not entirely accurate.  Evolution is not like shuffling a deck of playing cards or rolling dice.  It's more like a comparison sort wherein the results of each generation affects the degree of randomness in the next one, with failures falling away over time.

As the Miller-Urey experiment demonstrated in the 1950s, it is possible for complex organic molecules to form in a relatively short time.  Now extend that process over billions of years, with a bias towards complex structures gradually forming.

I fully expect to see DNA synthesis in a laboratory setting in this lifetime, sooner rather than later.

Random mutation is proclaimed to be the engine that drives new genetic information. It has also happened in the remote past, so I think that sentence was accurate.

The Miller-Urey experiment is rarely discussed in origin of life literature anymore because they used conditions that are now believed to not be accurate of the early earth. And yes, they produced a few amino acids, but once again this is far from the nucleotide based code of life. And the breaking of both peptide bonds and phosphodiester bonds (protein chain and DNA chain bonds, respectively) is energetically favorable, so I don't know that any sort of accumulation of these molecules would have happened. 

We already see DNA and RNA synthesis all the time in laboratories. In fact, they often produce artificial guide RNAs to direct CRISPR-CAS9 proteins to edit DNA sequence when they are genetically modifying organisms. The problem is when they try to do it without inputting information or intentionally directing which sequences should form.