VEVOR Mini Lathe "Ragrets" (my regrets)...

hammering a spindle out is perfectly fine long as you have a soft material between then hammer and spindle, make sure each blow is done carefully so your hitting it straight on and that the soft block is being held flat to the end of the spindle. Alternatively if you still not conformable with the hammer way put long bolts through your spindle nose plate with the head facing towards the tail stock with a nut & washer on the inside, hold the bolt head still and slowly move the nut to apply pulling pressure and make sure you apply pressure evenly between each bolt.

Just a block of wood on end of spindle and some taps with a hammer. Just remember it's a simple piece of equipment it wasn't made in a rocket engine factory.

We'll see what Vevor says (Monday, hopefully?) but.... assuming this is in agreement with Vevor... this is what I'd do. Possibly obvious, but here goes: Take a piece of pipe large enough to fit over the chuck, and long enough to get the chuck-side bearing out. Put this over the chuck and resting against the headstock casting. Some large rubber bands could be handy to keep it in place. Get a piece of steel with a hole in the center to bridge over the pipe., and another one to bridge over the far end of the old spindle. Into the holes in the bars, put a section of all-thread, and then put some nuts on both ends. Turn the nuts to put tension on the all-thread. This should result in pulling the spindle out the front. of the lathe. It may damage the front bearing, but that will be not reused anyway (there's a new one on the new spindle). It may also damage the old copper ring that's press-fit on the spindle, but again, there's a new one on the new spindle. Installation of the new spindle should be the reverse; except that you'll pull the new spindle in with the two threaded rings that you originally removed from the old spindle. You might need to flip the improvised puller around backwards if there's not enough threads on the new spindle to start the threaded rings before it's pulled into place. As for raw-greets.... the only reason I wouldn't have bought this particular model is the direct-drive motor arrangement. That leaves you dependent on Vevor's electronics to drive it. I would have chosen one with a separate motor with a belt drive, so that any off-the-shelf motor & controller can be fitted. I suppose trying to retrofit a pulley onto the spindle might be possible if you have a working mill at the time with a rotary table; so you could modify a cog pulley (aka, timing belt pulley) of the right size to attach to the gear that is driven from the spindle that turns the threading geartrain.

You need a press and a bearing separator

If they are made by the same factory, could you get a schematic from another brand's version? The important parts should be the same. Maybe there is online support/forums for their brand that you can use to fix your problem? I doubt my suggestion will help, but it might be worth giving it a shot. Best of luck.