You want to compare with a t-test or anova. How do you test the null hypothesis that the treatment has no effect?

Do you claim that it is possible to do this without first assuming that the two groups would have the exact same average if there were no treatment effect? If so I would like to learn your new method.

You should study some statistics. You seem to some (very) incorrect ideas about what the tests mean.

This is how it works. In a randomized study scientists will assign subjects two a treatment group and a control group. As you might guess assignment to a group is done randomly.

Now we go to one of the big misconceptions you seem to keep going back to. You state that scientists assume "treatment group and control group were exactly the same at baseline." They do NOT! On purpose they are creating random groups. They are making no effort at all to make the groups equal and in fact if they made any effort to make the groups equal it would invalidate the math behind the statistics and the experiment would have no real value.

They have two groups and they are as sure as they can be that the two groups aren't equal because groups were assigned randomly. They do whatever it is they want to do and then they measure whatever it is they want to measure. Statistics tells the scientists how likely it is that any differences they see between the groups are caused by random chance. In other words, statistics might say something like, "If the treatment had no effect at all we'd expect to see results like this x% of the time just based on the randomness of group assignment."

At no point in this process did the scientists assume that the treatment group and the control group were exactly the same.....

And if you want to learn this stuff you most certainly can. Pick up a cheap textbook on statistics. Read it and try to understand it. Be careful to make sure that you are learning not just how to run a t-test, but the assumptions that are built into a statistical model.