The phrase marks a specific routine time; it's about when something happens rather than what or how. She reads the newspaper first thing every morning.
Pro Tip 2/3
Emphasize Routine
Used to stress a habitual action done consistently at a certain time. I check messages last thing before bed.
Pro Tip 3/3
Not Literal
Sometimes it's not literal, just indicating early or late in a time frame or sequence. Finish your homework first thing after your break.