Assuming that "G" and "H" are the only stretchers that are glued to the legs, I would start with placing a 1" thick spacer under all the cross pieces and not the legs. IOW, have all the parts level.
Have a good framing square and a tape measure handy. Make sure "D" and "E" are the exact length, as well as "A" and "C". Figure the length of the distance for "F", and see if the combination of "A" "B" and "C", including the side gaps for "B", equal "F".
If you haven't done it yet, test fit all the parts and make sure all the dowels have a slip fit, and there aren't any hangups due to a long dowel, or a crocked one. Dowels and holes should be well aligned and parallel.
I would first glue "D" and "E" to "F". Then glue "F" to the legs. You will have to do a bit of squirming and some slight gentle twisting to get the other sections to seat. Glue "A"to "D", and "C" to "F". Then gently open the frame just enough to get "A" and "C" into the legs. I would use a bar clamp to press the parts together.
Use the framing square to check all the corners for square. Use the tape measure to check corner to corner equality in length measures. When done, install corner braces like below picture that you would have already made up and have them ready for installation.