2 Affinity from Servomachinery (via 25xp).
1 Affinity from Genetic Mapping (via 12xp).
1 Affinity from Might virtue.
1 Affinity from quest.
1 Affinity from excavation.
Pick from those, but note that since the the xp requirement increases with each Affinity level you need to grab the Servomachinery xp before the direct +1 Affinity sources if you want two Affinity points from it.
The top three are guaranteed, but are the slower sources of Affinity points. The quest source is semi-random (you are guaranteed the Affinity point eventually, but since the point of this is to do it quick...), while the excavation source is almost completely random (it is highly likely there are a good few on the map, but your chance of getting them isn't), however, the quest and excavation are by far the fastest sources of Affinity points.
Therefore, the quickest way to get the four Affinity points (and the desired battlesuits) is to beeline towards Servomachinery (using free tech as appropriate), then grab the quest Affinity point and the excavation Affinity point. However, every part of that has randomness involved - the institute quest may take a long time to pop up, the quest may not be the Alien Nests (and so take a fair while to complete), and the excavation Affinity point may never turn up (it is a random reward from the random progenitor ruins excavation, if I recall right).
On the other hand, the slowest you do it in is sort of capped at least - beeline Servomachinery, grab Genetic Mapping, grab Might Virtue.
So, while you are guaranteed at least fairly fast battlesuits (on Strategic Balance) it really is quite random as to just how fast you can get them, within a range of somewhere between 50 to 100 turns, without much control on your part.