What is the best approach to test a new PCBA?
So you went through weeks of schematic design and PCB layout design
and Sent files over to fab house.
Now, you got the PCB from FAB house.

Basically you learn from your mistake. That mistake is: don't ship any design out to a PCB manufacturer without simulating the circuit to death and re-fixing the schematic/PCB as you find design/performance/functionality errors.

What is the first step you do when you get PCBA? What are typical
tests tes that you follow for testing?

If you'd have simulated the design as advised, you would have already developed a series of tests (as guided by the ways in which the simulation tests developed) and, you would apply those tests right now. That's a professional approach to the situation; you already know the testing based on simulation - the sim would have uncovered the potentially weaker areas and those are what you should focus on now.
But because you didn't you are left scratching your head when in fact this could have been sorted out weeks earlier. Simulation saves between an average of 1 and 2 board iterations per design in my experience. It's a no-brainer - get used to your circuit before committing to copper. There is no economical alternative given that simulators are basically zero-cost these days.

intention here is to learn about best practices from people who are
working industry for years.

Well, you asked!!