Here's some drills that may help.
Basically, you are spoiling yourself by allowing all the time in the world to bring up the gun, squint down the barrel and fire at leisure. We have to break your comfort zone so you can learn combat tactical shooting basics. Get somebody to show you a correct grip if you don't know what it is.
A timer would help but is not vital now.
Stand at about 7 yards from a plain target with no aiming point, such as an IDPA target of a plain piece of cardboard. Take a firing grip on the gun and hold it about 45 degrees down.
Bring the gun up smoothly and as soon as you acquire the front sight on the target, fire. Repeat over and over. Concentrate on seeing the front sight, but don't allow yourself time to squint and pause. Then double tap. Then move on to the drawing and firing for speed.
In spite of your "not being ready" suggest you go to an IDPA match and tell them you've never done it before. They will let you just walk through the stages without trying for speed ( a good idea at first anyway).
The NRA personal protection courses are great training for learning tactical basics, also, including drawing and shooting from a variety of positions.
YouTube - How to shoot a pistol.