This is how I did it:
1 carrier, 1 bomber, 1 tank
2 tanks, 3 inf, 2 art from Bul/Rom to Ukraine
4 tanks, 2 inf, 1 art from Czech + Poland to East Poland
3 inf, 1 art, 2 fighter from Berlin via transport + Poland to Baltic states
1 fighter, 1 sub from NW Europe to SZ 6 (UK destroyer)
2 subs, 1 fighter from Norway to SZ 2 (UK battleship + trn)
2 tanks, 2 inf, 1 art, 1 bomber from France/Morocco via transport + Libya + Berlin to Egypt
1 fighter from SZ 2 to Norway
2 fighters from Baltic States to Bulgaria/Romania
1 fighter from SZ 6 to SZ 5 (carrier)
1 bomber from Egypt to Libya
2 inf from Germany to Balkans
1 inf from NW Europe to France
Try to attack Ukraine?
Germany has at least 2 inf, 1 art, 2 tanks left. Russia can attack with 5 inf, 1 tank. This is a 22% chance of success. I suppose Russia will not do this but rather boost the defense of Caucasus. This is the build that give the highest possible defense to Caucasus, although infantery + artillery would probably be better to ensure retaking Caucasus on R2:
2 fighters, 2 tanks to Caucasus
1 inf from Eastern Ukraine to Caucasus
1 Inf from Belorussia to Eastern Ukraine
2 Inf from Kazakh SSR to Caucasus
2 Inf from Novosibirsk to Kazakh SSR
3 Inf, 1 tank from Russia to Caucasus
They cannot reach Caucasus with defensive units except 1 bomber. I suppose UK will not do this.
UK can attack the baltic sea but will only have about 27% chance of success if you managed to sink the destroyer.
1 trn, 1 inf.
Attack Caucasus with 1 inf, 1 art, 1 battleship, 1 cruiser
Attack Caucasus with 2 bomber, 2 fighter, 7 tanks (1 from Egypt via transport), 3-4 inf (1 from Balkans via transport), 1 arty.
Chance of success is above 95%. Number of surviving attackers depends on how ferocious the Allies did defend Caucasus. If the British did not land their bomber and the Russians built infantery+artillery instead of fighters + tanks, up to eight(!) units will survive the battle. If you sacrifice the two fighters, depending on Allied strategy two to six tanks will stay in Caucasus.
1 tank from Germany to Balkans.
Possible continuations include an italian attack on Caucasus with two loaded transports, 1 ftr, 1 battleship and 2 cruisers on I2, reinfoced by a German shipment of 1 inf, 1 tank.
I have tried this opening in an internet game. In G3 I had a 95% chance at Moscow but failed. The concentration of tanks in Eastern Poland allows you to shift targets to the north in case Russia does not take back Baltic States. But even if Russia does so - the 3 inf. in Finland plus your transport and the carrier loaded with two fighters can put considerable pressure on Karelia, and it is possible that you will take Karelia and Caucasus at G2.
What do you think?