If you want to see where your ship is actually facing (not what’s displayed sometimes) use the tactical overview and observe the arrow. If you’re not moving there is no arrow.
Advanced players overshoot their alignment many degrees then push warp as the arrow is going over their intended destination, or simply use ‘the force’ because they’ve done it so many times it’s second nature. Doing this will make aligning with a prop mod much faster.
To take it to the next level a right angle warp from full thrust can be done in incredibly little time in large ships by combining this method with timely deactivation of the prop mod manipulating your max speed and through this your current % speed.