Could we have created and 'distributed' a variant faster than vaccines?

Omicron would have been absolutely devastating in the early days of the pandemic. Remember, we didn't have enough masks, no treatment, no vaccines, limited testing, unprepared hospitals, limited knowledge about the spreading mechanisms and a completely vulnerable population. Omicron is far from harmless, I've seen people saying that it is as deadly as the original Wuhan strain, so imagine the first wave, but 10 times higher. A Delta first wave would have been worse, but an Omicron first wave is still a nightmare scenario.

Now for the possibility to do it. Remember that vaccines took months of testing before getting approved, which is way faster than usual. And yet, with a vaccine, you don't have to worry about spread, mutations, etc... If you inject a really bad vaccine the worst that can happen is for test subjects to die. Now, try working with a live virus instead, you realize that your "safe but easy to spread" virus is not that safe after all, oops, no recall possible, you just killed millions of people. And even if your virus really is safe, viruses mutate, and despite what many people are saying, not always to become less lethal.

Really, I think we are lucky that Omicron turned out the way it did, it could have been much worse and it can become much worse. I don't think we should look further than that, it is just luck.

Even with ethics aside I think you would have to address the legal challenges assuming you are taking official channels to do this. Technically labs could release a variant that matches your criteria. There are some circles that believe Omicron was just that but AFAIK there is absolutely no empirical evidence to back that up.