The hinged-stick idea that David Etter proposed is a nice, simple one.
Being 1/2 of a scissors jack, it does provide mechanical advantage.

However, the farther the stick is from straight, the less advantage it
provides, so a hinged stick braced between the poptop, or lift lever,
might not provide enough advantage to get things moving. However, one
could just sorta lean into it if it was sufficiently strong.

Or maybe use a shorter one between the poptop's lift bar and the front
edge of the upper bunk platform to get things moving, then apply that
longer stick when things are halfway up. Something like that, anyway.

I was going to propose pulling, instead of pushing, by using a block and
tackle connected to the lift bar to pull it forward when someone pulls
on a rope, but it still needs a sky hook: the other end of the rig would
want to be connected to a point somewhere between the upper (poptop) and
lower (roof) hinge points in order to pull that bar forward and up.
Maybe someone else can see a way to make this idea work.

--
Mike "Rocket J Squirrel" Elliott
71 Type 2: the Wonderbus
84 Westfalia: Mellow Yellow ("The Electrical Banana")
74 Utility Trailer. Ladybug Trailer, Inc., San Juan Capistrano
KG6RCR