The answer to this OP IMHO, is to be found in Talmud Kiddushin 80a. The name of the "sugya" (topic) is "Soklin v'Sorfin al Ha'Chazakos" ("We stone and burn the accused because of a [strong] presumption of established evidence")
The Gemara there explains that the Court has the legal power and obligation to stone and burn the accused (finding them guilty of a capital offense) based upon a mere established presumption. How so?
If a man, a woman, and a girl live together in the same family household as man and wife, while claiming the child to be their biological product, we accept the absolute fact that they indeed enjoy such relation.
Now, if witnesses come and testify (years later when the girl becomes an adult) that the father (just now) committed incest with the daughter; then the Court executes them both (father and daughter). We do not say in their defense that perhaps he is not the real biological father of the girl.
This Gemara is based on the Torah itself. The Torah authorizes and requires that someone who strikes their father be put to death. This is regardless of the fact that one can never actually absolutely prove the identity of someone's father in Court.
So here you actually have a case in the Torah where Judaism teaches that even if you do not absolutely know something, you may still impose these rules on others in the Torah's name.
But, the OP is asking how we can impose things upon others "if we are not absolutely cetain" Judaism is true? If so, we cannot simply quote the Torah to prove how we can impose the Torah. That would be the fallacy of circular reasoning.
Lets step back and try to show that accepting the Torah (even without absolute proof) in the first place is considered to be following known objective truth.
Rene Descartes was a French philosopher (1596 - 1650) ("I think , therefore I am") who proposed a way to know if something is absolutely true or not. It can be expressed like this:
Proposition A is true, if you cannot find any alternative to A that could be true instead of A.
Example: Is it absolutely (known to be) true that I should take a dose of the prescription drugs in this bottle the doctor gave us?
Answer: You cannot say it is absolutely true, because the pharmacist may have accidentally switched the right medication, for poison, when filling this prescription.
Unless you can certainly eliminate all alternative possibilities, you can never say something is absolutely true.
Although, this definition (known as "Cartesian Proof") seems foolproof in theory, it breaks down when applied to the practical world as a thresh-hold for initiating responsible action or belief. Examples:
1) I woke up this morning and met my son at breakfast. He asked me for pocket money. I decided not to give him the money because maybe he was just my son's doppleganger, or an alien?
2) Although I feel and understand murder to be wrong, I have no absolute proof that it is wrong. So I have no right to condemn or judge murderers.
3) I need to stay home today, because there may be a lion in the streets and I have no proof that I will not be eaten.
As you can see, Cartesian proof will even have you question if you are actually awake, or just dreaming that you are. (Descartes actually asks this himself!)
So, we have established that anyone holding their beliefs and actions to the standards of Cartesian, or "absolute" proof of truth, will probably find it very hard to remain sane and live a normal life.
So, there is no such thing as absolute certainty; and that is OK.
What we need is to try our best with the resources we have, and the knowledge available, to make the best possible decisions in life that we can. We need to define "what we know to be absolutely true", by the best possible facts we can find, that make the most sense. Then, the stronger the facts, the stronger will be our sense of believing in what we hold to be "true".
Now the OP did not ask us to prove the truth of the Torah. So, for the sake of the OP, and this exercise, we will treat the truth of the Torah as a given, as follows:
1) I have exerted myself to find the truth as best as I can.
2) That search has led me to believe that the Torah is true.
3) But, I cannot say I know the Torah is "absolutely true" with Cartesian proof.
4) However, since waiting for (such unattainable) Cartesian proof will cause sure madness and risk destroying the world etc. I have the obligation to choose responsible action and to go with the overwhelming proof I have found which has triggered my own inner belief and convictions based upon it.
5) Based on the above, my belief in Torah is now elevated to the level of "absolutely true" in effect and as far as I can tell. That is absolutely good enough and it is relevant and compelling as well.
6) The Torah itself also obligates me to act and impose, even upon others.
Conclusion: Therefore I am justified and obligated in living a Torah life and doing whatever the Torah says about imposing it upon myself and others.
The above applies ditto for condemning such people as Nazis. You do not need to be absolutely morally sure that Nazis are wrong to condemn them. Your knowledge about the evil of murder and hate etc. is enough to be considered just as good as absolute knowledge, even if you would not win a debate with your knowledge at Harvard.
Finally, if you do not really think you know the Torah (or any moral code) to be true, (forget "absolute" LOL) then the truth is, you are a bit lost. Under such circumstances, you should not be imposing life decisions upon others or yourself in a major way. However, life is not such a willing partner to your ignorance. Pretty soon, you will be faced with daily paradox situations forcing you to choose even if you are not sure. (unless you simply live in a cave)
Therefore, you need to still strive to work hard at learning, until you do in fact realize you have found a set of values that are true. Of course, I think you will find that it is the Torah.
(references to "you" are style and grammar, not assumptions about the particular person reading this.)
I hope this helps :)