We made that exact transition, and the limitation you describe is real - you can’t get anything out of GA, particularly at the granularity you’ll have with an alternative.
So it’s best to start early, because it’s a slow process.
It’s even slower if you don’t instrument the right events in the beginning, because you’ll wait a while to gather enough event data to perform an analysis, find you want to track some new event, and then need to wait even longer to have enough data for analysis. It can be frustrating, and a surprising amount of work.
If you want to build out your BI infrastructure in the mean time, you could always ETL your e.g. server logs into the data warehouse as a stopgap. It’s definitely not the same as the customer-centric setup that you get with Segment, though, unless you have some advanced logging already set up.
Are you a paid GA user? If that's the case, you can ingest your data into BigQuery. Otherwise; you can't export the raw data, the only option is to export the summary data (number of unique users per hour, day, week etc.) from GA to your Redshift cluster via an ETL tool such as Segment.
Seems like using Segment here is probably the least effort solution for future events, although it doesn't address ETLing past GA data into the warehouse. Curious if anybody else has had to deal with a similar situation.