Alternate History

We would have been fighting the Japs until 1947 to invade the home islands. Each side would have lost a million men on the beaches. So jets would watch and let us weaken while they develop bio weapons. We would prevail eventually but be way behind Stalin. And we would not have been there for other countries who would be gobbled up by the Soviets. The world would be more totalitarian, poor, and backwards.

There's a theory out there that the bombs didn't actually affect Japan's decision
https://foreignpolicy.com/2013/05/30/the-bomb-didnt-beat-japan-stalin-did/
And I kind of believe it because if you think about it the US was bombing the snot out of Japan months prior to the bombs being dropped. Tokyo was hit a lot harder with the conventional weapons than Hiroshima and Nagasaki were but even though it was the capital Japan didn't surrender because of it.
Not saying I 100% believe it, but when you think about it it really makes a lot of sense

Well if we didn't have nuclear weapons there would have been no Hiroshima or Nagasaki. That wouldn't have changed really anything other than that the Soviet Union would be able to take more credit for ending WW2, so it would have made them look stronger than us. I don't really know much about bioweapons but I'm sure that during the cold war, both sides would try to get an advantage over the other and that might possibly have led to more development of bioweapons.

In this alternate timeline, it would probably be the U.S. catching up to the Soviets on bioweapon technology, rather than them catching up to us as it was with nukes. Not that there was much time difference, and this alternate timeline would be the same. The Soviets had a biological warfare program since the 20s whereas the U.S., while it did experiment somewhat with bioweapons in WWI and the interwar period, didn't have a biological warfare program until 1943. The bioweapon capabilities of the U.S. and Soviet Union would quickly become evenly matched during the early stages of this alternate Cold War, obviously because this would be what the arms race would be focused on instead of nukes.

https://en.wikipedia.org/wiki/United_States_biological_weapons_program

https://en.wikipedia.org/wiki/Soviet_biological_weapons_program

As you said, both sides would be looking to get any kind of advantage over each other. While bioweapons could be the primary avenue for that in an alternate timeline without nukes, other unconventional warfare programs would be viable such as kinetic bombardment or microwave weapons.

https://en.wikipedia.org/wiki/Kinetic_bombardment

Thank you for the info, I did not know the Soviets were so far ahead of us on that

We would have gone to war with the USSR.