Pure speculation about the rest of the season and season 3. I have no special knowledge, but I'll make it a spoiler anyway.
[SPOILER]
First, the title For All Mankind is not incidental, so the peaceful exploration of space on an international basis is probably the theme and dramatic destination of the series, so I'm guessing that season 2 will end with the ASTP handshake in space. Season 3 to be about a US-Russian (or broader coalition) to Mars.
Conflict is presented as being embedded in higher level politics while cooperation is tentative and conducted at a very interpersonal level with small gestures of outreach. One is the ASTP docking mechanism, and the general dynamics between Margo and her Soviet counterpart, leading up to her warning him about the O-rings, against orders. This was complemented by the pep talk that the unnamed engineer gives to Danielle in Star City. Also Tom Paine was on KAL 007 because he was exploring an Asian space alliance. That was at an official capacity, but was presented as tentative, initial.
There's also a bit about Ellen thinking of leaving NASA because she believes that private enterprise is the future of space exploration. That's just a thread left hanging at the moment. It could be a turning point as Tom Paine is killed and she's suddenly made acting NASA administrator.
On the other hand. Plenty of talk about Pathfinder being armed and speculation that Buran might be (interesting that in this timeline Buran is an exact copy of the American shuttle, including having solid boosters. I suppose that enables the thing with Margo and the O-rings). Chekhov's Law is certainly going to apply. If there isn't an actual space battle, there will certainly be a standoff, fingers on triggers, beads of sweat floating away from furrowed brows, clocks ticking and so on.
Everyone has an 'Oh God, what have we done?!' moment, Gorbachev comes to power in the Soviet Union and work towards walking back from conflict. ASTP becomes the gesture that ends the Cold War, perhaps in parallel with the fall of the Berlin Wall.
Also, Tracy and Gordo get back together.
[/SPOILER]
