Step 1: Read all 4 problem titles and first lines. Just titles and first lines.
Step 2: Mentally rank which one looks most approachable to me right now.
Step 3: Solve in order of my ranking, not the contest's order.

Sounds obvious. Most people I know start at problem 1 automatically.

Problem 1 is usually easy but sometimes it's a weird math/greedy that I'm not good at. Problem 2 is sometimes a standard pattern I know cold. Starting by my ranking instead of the list order saves me 10-15 mins per contest.

Also helps: drink water before the contest. This is non-negotiable.