There is a huge amount of misinformation on this topic, including in this thread, at the minute.
Some index funds have a very long horizon before they include them (e.g. a year). Others are "fast-tracked" (e.g. notably VTI). Most of those, however, are float-adjusted, so only the stock available for trade is considered part of the marketcap. So e.g. VTI / VTSAX will buy spacex relatively quickly after the IPO but at the float-adjusted weight of ~$75B because that's the % of stock available.
If you care alot about this, now is the time to understand how your index fund treats IPOs wrt to delays + float adjustment.
Do you have any suggested reading references?
Specifically, I do a typical 3FP and own VTSAX, but I don't read bogleheads or anything. True set-it-and-forget-it, but I do want to read more if things are shifting.