I’m wondering if the question is about receiving the plenary indulgence for devoutly assisting at a priest’s “first Mass before the people on a chosen day”. (Manual of Indulgences n. 27 under Other Concessions)
§ 1.47 Plenaria indulgentia conceditur
1° sacerdoti primam Missam coram populo statuto die celebranti,
2° christifidelibus qui devote eidem Missae astiterint.
The wording, at least in English, is very odd. It seems to imply an indulgence for assisting the first Mass a priest say each day, but the second half of the concession is about Masses on the priest’s anniversary of ordination. So, I think it’s safe to say it’s referring to the priest’s first Mass.
This may be the source of the “first Mass” (primam Missam) terminology as well.
Pax Vobiscum