It’s a good idea to do that where you can, but some engines mount their oil filters sideways or even upside down.

In these cases, some cars have a “clear flood” mode that will let you crank the engine without it starting. You can use this to pump oil though the engine for 5-10s and help prime your oil filter. For instance on Subarus you can hold the accelerator to the floor while you try to start it to engage this mode.