[Stiglr]

Select the "front facing" surface(s) and when you extrude them, the front face should remain. if you do multiple extrusions, the interim faces will be left behind too.

(even better if you combine all surfaces to be extruded into one single surface first, extrude them as one face, and then (re)do a triangulate when you're done modifying it)

For things like cylinders, thre's a Cap Ends box you need to check to avoid merely making "tubes".

Or, actually...

It's possible that when you redrew objects from your Illustrator guide that you created poly lines only? Select all the vertices on the front face and select Vertices/Create Convex Surface/Object. That will create the face.