Depending on the userbase of the site, simply checking for @gmail.com at the end, I'd bet, would result in a quick win, as well as restricting the username's alphabet to allowed Gmail characters.
The other optimization I'd guess at would be to async/thread/process the checking before and after the @ symbol, so they can run in parallel (ish). Extra cpu time, but speed > CPU cycle count for this benchmark.
[Rehashing an old comment]
In the math department, we had a Moodle the students in the first year of my university in Argentina.
When we started like 15 years ago, the emails of the students and TA were evenly split in 30% Gmail, 30% Yahoo!, 30% Hotmail and 10% others (very aproxímate numbers).
Now the students have like 80% Gmail, 10% Live/Outlook/Hotmail and 10% others/Yahoo. Some of the TA are much older, so perhaps "only" 50% use Gmail.
The difference is huge. I blame the mandatory gmail account for the cell phone.
So, checking only @gmail.com is too strict, but a first fast check for @gmail.com and later the complete regex may improve the speed a lot in the real word.
Maybe I am old, but I like to keep as much communication as possible going through the university email. It just feels more official somehow.
Tell us you used to work at Google, without telling us.
"simply do X" is such a programmer fallacy at this point I'm surprised we don't have a catchy name for it yet, together with a XKCD for making the point extra clear.
Tell us you don't actually work with any Google engineers... blah blah blah
The trope is "At Google we..." and then casually mention "violating" the CAP theorum with Spanner or something.
It is simple, and I really do hope any first year CS student could extract a substring from a string. Have LLMs so atrophied our programming ability that extraction of a substring is considered evidence of a superior programmer?