You can build the most compact 1 per second builds for Science Pack 3 and Production Science Packs with Assembly Machine 3, but you cannot make Assembly Machine 3 until you have research Automation 3. This research requires Science Pack 3 and Production Science Packs.
So before then, here's a build using only Assembly Machines 1 and 2 that will produce 1 Science Pack 3 per second.
Note: The blueprint includes entities from Creative Mode, to simulate what needs to be on each half belt, so you can test it if you wish. They will be ignored if you use the blueprint in vanilla factorio.