> the entirety of that data needs to be loaded into my program

What? No. I'm not saying the entire Google search index is feasible, but you can do a lot. Here are some concrete numbers from what is now considered an "old" paper (2022; it has been improved since then)

https://eprint.iacr.org/2022/949

To make queries to a 1 GB database [in a scheme called DoublePIR] the client must download a 16 MB "hint" about the database contents; thereafter, the client may make an unbounded number of queries, each requiring 345 KB of communication, and a throughput of 7.4 GB/s/core.