I was playing LAN with two other people and the first time we managed to get in, but it took very long for us all to synchronize past the training phase and into the Von Braun section.
It takes up to 15 minutes to load up a game.
Is there anything to be done?

multiplayer is bugged. it might, or might not work.

As voodoo47 pointed out multiplayer was/is extremely buggy mainly because it was a last second tact on "feature" EA brass wanted slapped into the game just because.

Anyone got a solution?

There isn't a soution, it was a bolt on with a patch, and not build into it from the start.

What you see, is how it is.

It was not part of a patch, it was there with the initial release of the game.

it was part of patch 2.3. does not change the fact that it's very buggy.

So there's no good consistent way to play coop here? Not even by using alternative solutions such as Hamachi?

I'm playing through the game for my first time single player, but it honestly seems like it would be a lot of fun in coop on a 2nd run. Specializing in stats and perhaps playing on one of the higher difficulties seems like it would be an interesting experience.

nope since it was a last minute tact on feature it was poorly coded and so short of someone recoding or patching up the multiplayer all together which, short of nabbing the source code, wont really happen.

I can't solve the problem but I can confirm that the criticisms of multiplayer support are overstated. The day the multiplayer support was released, years ago, I started a co-op game with a friend over a 64k ISDN link, and over several evenings we played the whole game through that way. It was a TON of fun, and worked pretty much fine, in fact I'm not sure I ever finished the game in SP mode. I don't remember any particularly long sync time. Perhaps I'm only remembering the good bits, but if it was many minutes I'm sure we'd not have kept playing.

I'm planning to repeat the experience - although at the moment I can't get the GOG version to run at all, SP or MP ! So as you'd expect there's clearly a number of problems with modern platforms - but if they can be worked round, the MP mode should give you a great time.