Historical SPX Intraday data with volume

Last time I checked, algoseek has that kind of data. Their S&P 500 Trades and Quotes+minute bar data set contains OHLC, FINRA volume and etc. You can find a sample of their dataset here

If you have an Interactive Brokers account, you can get historical intraday index data, including SPX, through their API.

Many developers find using the Interactive Brokers API to be a challenge, especially for collecting large amounts of data. If you want a more turnkey access, you can check out QuantRocket, which provides data collection tools on top of the Interactive Brokers API (among other data providers).

Disclaimer: I'm affiliated with QuantRocket.