Options - large block purchases

One thing doesn’t add up in Options in my mind – just trying to see if someone can explain it. Say someone has placed a huge, large Buy to open for a Call option. By Huge I mean extremely large so that it is 100x larger than the normal volume for the given strike/expiry. (Say like $1B worth as an example, whereas normal Vol is $10M for the sake of argument). Now as we know normally a large block like that causes the price to move up, as it’s being filled. However, the underlying is not moving at all, or even is going down against the option. So as this person is getting filled (a limit order), I assume there would be either enough liquidity on the other side (sellers) to help sell to him eventually, since the market is falling against him, or he will simply not get filled fully at all? But presumably he should eventually, no matter the size of the order? Or will there normally be liquidity issues, even in popular-strike-values at Index Options (like SPY)?

Note an order of any magnitude on the Options side will not directly affect the underlying ETF/Stock at all, as it’s only a bet against it on the sidelines. It may get noticed, yes, and have an indirect affect on it or raise some eyebrows, but will not directly affect it. So if there are not enough participants on the sell side of this, will market-makers provide the liquidity for this option to get filled at all? Or it will just stay unfilled? But if not, the price of the option has to fall, as the market is falling, so this order will have to be fully filled eventually?