VRAM is used to load game textures and other data into the GPU where it can be processed the most quickly. VRAM usage goes up with increases in resolution and certain game settings.
Frame rates are linked to how many times the GPU can send out a complete frame of this data in one second. The less processing power that is needed to render a frame, the more frames can be rendered in one second. Thus, being able to reach 144 Hz is dependent on:
How fast your CPU and GPU is (cores, clock speed)
Compared to:
The amount of detail you are asking your GPU to render.
There is no direct correlation between VRAM and frame rates. If your games are causing you to run out of VRAM, that will reduce frame rates, but you do not need a specific amount of VRAM to run games at a certain frame rate.
Now, whether a GTX 1650 can run a game at 144 fps is another matter entirely. Most likely you will have to play at lower resolutions with lower detail settings to hit 144 fps; the types of games you play and how new they are will affect your results as well. This is not due to VRAM, but due to the GTX 1650 not having a whole lot of processing power, and as a result, having difficulty rendering a frame of just about any modern game 144 times in one second.
Besides that, in order to run a game at 144 fps you're going to need a decent CPU. Your CPU is responsible for feeding data to your GPU; the more frames you want to be rendered per second, the higher the clock speeds your CPU needs to be capable of.