So you haven’t done the calculation.
You don’t even seem to know what you are calculating, how to calculate it, or what the inputs would be. It’s just your gut feeling of what the result would be.
Which leads to this: Mathematical claims without calculations can be dismissed without calculations.
Claim dismissed.

Why would anyone assume that cells in different organisms are produced one at a time? Are the bacteria forming a queue with each bacterium being prevented from dividing until after the previous one divides?
I said I would endeavour to make meaningful points, so here are two calculations.
First, the number of organisms you have said have ever existed (“Thee ae literally millions if not billions of creatures who have lived and died without leaving some sign of their existence”) divided by your estimate of how long life has existed (“3.'5 billion years”):
nb orgs / 3.5by = n/3.5 ~ 1 organism per year
One organism per year doesn’t seem unreasonable even with your ridiculous assumption that life reproduces serially rather than in parallel.
Though that’s using your vast underestimate of the number of organisms that has lived, so it’s GIGO.
Here are some sensible numbers:
Total number of living cells on earth: ~10^30.
Minimum time for an E. coli bacterium to mature and divide: 20 minutes.
So given optimal conditions, one bacterium could produce as many cells as there are currently on earth in (1/3)*log2(10^30) = 33.22 hours, or less than 2 days.
Obviously there will never be optimal conditions, but equally obviously 3.5by is a lot longer than 2 days.
So producing the number of organisms we have today is not a problem.
3.5 billion is, coincidentally, roughly the size of the human (haploid) genome, so producing the human genome from a genome consisting of a single nucleotide would require on average one mutation per year, even if all mutations are single bit insertions or duplications rather than multi-bit or even whole genome ones. Also coincidentally, one mutation per year is in the same ballpark as both the human and the E. coli mutation rates. So generating a suitably-sized genome isn’t a problem either.
Unless @RichardG produces an actual calculation that shows what the problem is, rather than doing the forum equivalent of waving his arms about and sputtering incoherently, nothing needs answering.