But your broader point is correct. Cold starts are a challenge, but they're one that the team is constantly working on and improving. You can also help reduce cold-start time by picking languages without heavy VMs (Go, Rust, etc), but reducing work done in 'static' code, and by minimizing the size of your container image. All those things will get less important over time, but they all can have a huge impact on cold-starts now.
Another option is Lambda Provisioned concurrency, which allows you to pay a small amount to control how many sandboxes Lambda keeps warm on your behalf: https://docs.aws.amazon.com/lambda/latest/dg/provisioned-con...