When changing the oil does the oil filter immediately fill up when oil is added or does it not fill until the motor started. ?

Motor has to start. Sump picks it up and sends it to the filter then out to the rest of the engine.

Put some oil in the filter before you spin in on. That reduces the time for the engine to make oil pressure. Might be messier on a six, but it would still work.

Don't pre-fill the filter, logic is if there's any air in the pump or pickup tube it will be pushing air against the oil in the (pre-filled) filter making the pump slower to prime. Our pumps are very good at pumping oil, but they're shit at pumping air.
The dry filter will fill incredibly fast and you should see the idiot light go out in 2-5 seconds.

If you want to be real anal dump and fill the oil first, then R&R the oil filter separately afterwards.

Just rambling.... I have a type 1 with full flow, remote filter and a 3.5 quart deep sump, if you pull the filter and oil at the same time you lose the prime have to fuch around, take a hose off, turn the engine backwards, while pouring oil in the hose end... to prime the oil pump. PITA, but if you use the above method it doesn't lose it's prime.
Same logic on the type 4, if you dump the oil and filter same time you get air in the pickup tube and it often takes a couple seconds longer for the idiot light to go out.
Next time do the oil and filter separately and see if I'm bullshitting you or not.

If you've been changing the oil and filter at the same time or even pre-filling don't worry about it (but please stop pre-filling), as it's still well within the safety margin as long as the light went out. Type 4 the pump doesn't have to lift the sump oil so prime is never really an issue. Only exception is when it's a new pump or engine, you have to grease the pump gears so that it will pull air and prime faster.

Learn something new everyday. I've never heard that as a reason to grease the gears. Makes perfect sense, I was told to grease the gears anyway, even if it comes lubed. Now I know why.

You can always set conditions so the engine will not start (pull fuel pump relay, pull coil lead, etc.) and then crank the engine until the oil pressure warning light goes out.

Why?

I never prefill the filter, but after I drain all the oil, I add a few ounces of new oil and let it drain through, pushing any old puddled pan oil out. You'll see it coming out the drain, black first, then turns clear. Yeah, it's anal.