Most index funds, and essentially all that matter economically, hold stock in proportion to the free float, and not the total market capitalisation. See
https://en.wikipedia.org/wiki/Public_floatSo if SpaceX only sells 1% of shares in the IPO, and the rest are locked up, then these index funds will only try to buy some fraction of this 1%.
For simplicity, let's assume about 25% of stocks by value are held by index funds. In our case, that would mean that index funds would buy 25% of 1% of SpaceX, or about 0.25% of SpaceX's market capitalisation. For simplicity, assume a SpaceX market capitalisation of 2 trillion USD, so that would be 5 billion USD. A big sum for you and me, but not all that much too worry about for the index fund industry and the stock market.
Later on, the lock ups will be lifted. That will increase SpaceX's weight in the relevant indices, but will also make sure that more stock is available to buy for them.
About the impact of short sellers: let me construct an exaggerated cartoon example. Suppose our index fund already has a 100 shares of SpaceX and wants to hold 300 more, but no else who holds SpaceX is currently allowed to sell for another three months.
Well, index funds are really, really keen on lending out shares to get a bit of extra revenue. So the index funds lends out 100 shares. They go to a short seller, who immediately sells them back on the exchange, where the index fund buys them. Now the index fund has exposure to 200 shares. 100 'real' shares it just bought, and 100 shares that the short sellers owes them. Well, the index fund can lend out the 100 real shares again, and repeat the cycle 2 more times, so that at the end they have 300 lend out shares and 100 real shares on their books.
In three months the lockups expire, and the short seller closes out their short position.
The above is an exaggerated stylised cartoon description, but it's not too far off what can happen in principle.
Well, the index fund would lend out the 100 'real' shares they have at the end, too, just to collect a bit of extra borrow fee on another 100 shares. So the index fund has an economic claim to 400 lend out shares, and doesn't currently hold any physical shares.
Other market participants can trade these 100 physical shares back and forth amongst each other (or loan them to each other, too) to help with price discovery.
There's also stock futures, where you trade the right/obligation to transact some shares at specific prices in the future. Economically, entering into a contract today to be obliged to sell shares in the future is equivalent to becoming a short-seller, but for regulatory reason you don't need to borrow the shares when selling futures.
So stock futures are another way to help with price discovery, even when there's scarcely any underlying shares available right now.