2011 IS250 Won't start
 

Hi everyone. So I'm having a weird issue with my 2011 is250. I got a full tank of gas yesterday and drove for a while (probably like 20-25 miles). Afterwards I parked the car and when I came back the car wasn't starting. It was getting into accessory mode but no crank or nothing. After a couple minutes it started. Then I drove for a while and had the same issue but this time it was not starting at all. To check if my battery is well connected I opened the hood and touched the battery terminal to see if the battery connection is loose. And then it started. The same thing happened today as well, wasn't starting, getting into accessory mode turns everything on but no crank no clicking sound but starts right after I touch the battery terminals with my bare hands. I took it to AutoZone to check the battery and they said the car has a healthy battery, alternator and starter. What could be the issue? Has anyone here faced the same issue before? I can hear the fuel pump working. Before I did the fill-up everything was fine no issues at all. I got 93 gas from BJ's and I fill-up from the same pump every time. I changed my key fob battery as well to see if it was the key fob but still same issue. Appreciate any help I can get.

Update: Changed the starter as my mechanic said he's 95% sure it's the starter. The car ran without any issues for 2 days and today the same problem came back.