Did the "Big" badge look like this?
If so, that denotes Volvo's "B series" OHV slant four, 1.8 liter displacement. If the "G" looked like a "g", then that would be the 1.9 liter slant four.
And did the car look like a 2/3 scale '48 Ford designed by a bright 12 year old? Probably a PV544:
In any case, I for one would love to see pics of it- I'm an unapologetic Volvo geek.