iPhone 4 Activation without SIM

You can't. And I honestly don't know what you would find useful in an iPhone that isn't even antique at this point. It's ancient, no longer supported, can't run any of the newer iOS versions, and won't work with most modern Apps.

It's time to say so long to that ancient relic and buy a newer, modern iPhone.

It is not possible.

OK. I hope it only cost a few pennies as it's totally worthless.