A few tips

Run the engine with the radiator cap off from stone cold to warm enough to open the thermostat.

As it warms up, and throughout the testing look, for strings of bubbles in the radiator neck that may indicate a leaking head gasket or crack. These will be more obviously a pattern of bubbles and not just gurgling splashing.

When the thermostat opens coolant should flow and you will see turbulence in the radiator neck. If it doesn't flow you probably have a thermostat problem. One thing that may help is to drill a 1/8" hole in the thermostat to help water flow around it. Many thermostats already have this. It makes sure hot water gets to the thermostat to open it.

If it flows well give it a minute to start warming up the radiator. Run your hand along the radiator feel for cold spots. If you have them it's probably a clogged/defective radiator.

If it is flowing well and the radiator is warmed up evenly you may have an undersized radiator or low coolant flow from bad water pump or restricted passage.

Pull the thermostat completely and see if it still overheats and if the water flows. No water flow is a definite clog or pump problem. This sounds dumb but is the water flowing correctly. Some water pumps push water in from the bottom and out the top of the radiator the factory pushed in the top of the radiator and out the bottom. Doubtful you have a defective water pump with the impeller reversed but I have seen crazy crap.

If you feel you need to flush the debris out of the block I have done it by popping a couple freeze plugs out of the motor. Preferably two per side and as far apart as possible. I use a garden hose to flush the crap out. It often can be done without removing the engine but it is messy. Since it is a fresh restoration you may want to have a fresh paint job on the engine and want to keep it that way. If it is a small block they have plugs behind the flywheel