What you want to do is create your transport unit(s) in the corner of the map (somewhere hidden from the player's view) and spawn the waves of units there too. Then order your spawned units to load into the transport unit(s). Finally, after they're done loading, move them to where they should be. This will give the illusion that the Transport units spawned fully loaded and ready to go.
I attached a map with an example of how you could do this.
There's some tricks in my demo map that allow you to make this work effectively. First, you want to turn off the unit collision temporarily for all of our spawned units so that they can stack inside of one another. This makes it easier for the Transport to load them. Then, and this is important, you want to go into the Object Editor and set "Movement - Group Separation - Enabled = FALSE" for ALL of your transport units. You only need to do this for the transport units, not the units that will be loaded into them. This prevents boats/flying units from pushing away (separating) from one another.
If you have any questions just let me know.