2000 Suburban 5.3L

My 2000 Suburban with 115,000 miles starts at the first turn on the key when it’s cold.

After driving for a while, shutting it down and letting it sit for 10 minutes it’s hard to start. The engine turns over normally but will not start unless I press the gas peddle a few time. After this it runs a little rough for a few seconds then smooths out.

If after running it I shut down then immediately restart it starts up fine.

No other engine issues once started, it runs normally.

Where to start?