How do pilots know when is the suitable time for taking off?

It isn't just once runway's cleared, the weather is within the acceptable tolorence, and ATC clearance is obtained, that the pilots determine it's ready for take-off, but also the pilot-in-command deems the aircraft itself and the crew (as well as the passengers) are physically and mentally ready to go. Pilots are also responsible to visually assess whether the surrounding environment is safe for the aircraft to take off. Imagine that the weather's good, the runway's cleared and you got the ATC clearance, but some birds are flying around the taxiway (though the runway itself really is cleared). What would you think?

Also there's no such thing called "Maximum Take-Off Speed". V2 is called the "Minimum Take-Off Safety Speed" which is calculated base on the Stalling Speed with clean configuration + 20% as safety margin. Aircraft can roll safely even though it exists V2.

They have to get a ATC ( air traffic controltower) clearance to do everything. There is always suitable for plane to take off , it just depends on the wind and the speed. They usually take off with headwind so the plane can get more lift.

when they go to a suitable speed for take off they will call out V1 (minimum take off speed) then they will call out VR or rotate (Speed which is good for take off) and the V2( Maximum Take off Speed) after pull up a few second

when wx (wind, viz, pressure etc) is within limit, the RWY is cleared for take off, and the Vr is reached.