That would be up to the developers I would think.
There are a few games set to release before the end of the year, as well as the promise that we'll get a free game once per month. With those, and the fact Google brought in 10 extra games the weekend before launch I expect it'll snowball. Here are the games for this year for reference:
Coming in 2019:
They never said it would be once a month they just said every now and then we would get a free game
@Sheaffer117 one of the lead figures at Stadia announced on Reddit that it'll be once per month. Link to the article for reference.
From what had happen with the '4k 60fps' streaming comment I hope they learn their lesson on gassing up the product and failing to deliver. Here's to hoping for those one free game a month.