the Soviet Rifle Sqd 43 starts producing in Jan 41, so by about March 43 there's a decent amount in the pool. Then & once every following quarter, go thru your Soviet Rifle & Motor Div/Bgds to upgrade their 41 Sqds, I found it convenient to do this by HQ formation (1st Banner Army, 17th Army, etc.), leaving the Region Fortress CD units for last. The Rifle Sqd 43 has 3 times the anti-armor & better than twice the anti-soft firepower than the 41 Rifle Sqd, so it's a 'must have'. The Motor Sqd 43 gets the 3X anti-armor improvement, but degrades a bit in anti-soft - it's the Motor Sqd 44 that you want.
Other than the infantry upgrades, there's not much to be done 'til the T-34/85 starts building in 5/44, but I'm stockpiling these for future use as replacements.
The really heavy death-star LCUs don't start arriving 'til May 45 (in my DBB_B game).