Can time spent living as renter prior to owning a home count as principal residence "use" time towards 2 years required for capital gains tax exclusion upon later sale?

No. You must both own and reside there in the same two year period. You don't need to live there consecutively for two years, but you do need to own it and use it as a main home for two years.

How your sale qualifies.   Your sale qualifies for exclusion of $250,000 gain ($500,000 if married filing jointly) if all of the following requirements are met.

• You owned the home and used it as your main home during at least 2 of the last 5 years before the date of sale.
• You didn’t acquire the home through a like-kind exchange (also known as a 1031 exchange), during the past 5 years.
• You didn’t claim any exclusion for the sale of a home that occurred during a 2-year period ending on the date of the sale of the home, the gain from which you now want to exclude.

Yes, that qualifies.

See Example #3 in the Regulation:

Taxpayer C lives in a townhouse that he rents from 1993 through 1996. On January 18, 1997, he purchases the townhouse. On February 1, 1998, C moves into his daughter's home. On May 25, 2000, while still living in his daughter's home, C sells his townhouse. The section 121 exclusion will apply to gain from the sale because C owned the townhouse for at least 2 years out of the 5 years preceding the sale (from January 19, 1997 until May 25, 2000) and he used the townhouse as his principal residence for at least 2 years during the 5-year period preceding the sale (from May 25, 1995 until February 1, 1998).

https://www.law.cornell.edu/cfr/text/26/1.121-1