Yep in the 60´s after a strike with a couple of hundred nuclear weapons, which is not what the OP was asking for. No nukes and 1983. And yes, the WP had extensive Bridge building Equipment but concentrating tat near the Elbe would give the routes for attack away. So you need to go over without bridges first, clear the west bank, than start building bridges (while at the same time somehow improving the abysmal road network of the GDR in the area, fend off any counter attacks, push Nato artillery units far enough away from the crossing site, establish a well working AA System at the site (and btw, make usre that not a large part of your mobile bridges has been blown up by arty and air attacks) then get troops and supply over, reorganize and then push through the (themselves reorganized) NATO defenses. And all this in 24 hours and in this time cover more than 80km of ground. Possible if the NATO troops simply waive red flags to greet the WP or if they are annihilated in nuclear strikes. Not in 83 without nukes.
Well, the nukes still fly....just not yet.