It is de fide catholica that "anyone whatsoever" (Lateran IV, Canon 1) can validly baptize. As long as that individual is using valid matter, form, and intent, he or she can validly baptized another individual. It is also de fide catholica that, for an infant, a valid baptism is always a fruitful one. Once baptized, such an infant becomes a Child of God, passing from darkness to light, and is at that very moment completely fit for Heaven and everlasting life.
A Catholic can have moral certitude that he or she was validly baptized. In nearly all instances, a Catholic is baptized as an infant by a validly ordained Catholic priest, a man who has been trained in administering the Sacraments of the Church and who has taken a vow to that effect. In addition, at nearly all Catholic baptisms, there are witnesses present -- the infant's parents and his or her godparents, plus many others. If there is a doubt about the baptism, it will almost certainly be detected, in which case the individual could be baptized again, at least conditionally.
For a Jew, Muslim, Buddhist, etc., could they ever have moral certitude that they were never baptized? How could they ever go about "proving" such an assertion, that something did not happen? As any first-year law student will tell you, it is far, far easier to prove the guilt of someone than to prove that person's innocence, that is, that the individual in question did not commit some crime. Trying to "prove a negative" is often very difficult, if not impossible.
Consider the perspective of the modernist Catholic who goes to an ecumenical meeting with the goal of making Jews "better Jews," Muslims "better Muslims," etc. That Catholic knows to a near-absolute certitude that he or she was validly baptized and can certainly have faith in the sovereignty of the One and Triune God that he or she was blessed with that sacramental grace. But, how could that Catholic possibly know that the other "Jews," "Muslims," "Buddhists," etc. in the room were not ever sacramentally baptized?
Consider the case of Charles Edmund Cullen, a nurse who administered lethal drugs to around 40 of his "patients" whom he was attending to. As a nurse, he was able to go from one job to another continuing his spree of murders over the course of many years almost completely undetected. If he had instead baptized his patients instead of murdering them, do you think that he would have ever been "detected"?
Now consider the hypothetical case of a young woman, a childcare worker in Saudi Arabia, the heart of fundamentalist Islam. Let's say that this young woman converts to Christianity, perhaps from hearing the Gospel on shortwave radio, the Internet, or from a friend. Having no Catholic priest available, she has a friend validly baptized her. Believing what she feels is the inspiration of the Holy Spirit, she begins baptizing infants born to Muslim parents, by the hundreds. Wherever she goes, she baptizes. Her friend does also.
Of course, we all know that non-Catholic infants get baptized. Canon 868 §2 states, "An infant of Catholic parents or even of non-Catholic parents is baptized licitly in danger of death even against the will of the parents." Still, a valid baptism for an infant, even if it's illicit, still confers sacramental grace. How often these baptisms occur is anyone's guess, but that they do occur is absolutely certain.
So let's consider the case of a validly (but, perhaps, illicitly) baptized infant born to Muslim parents (a sacrament that was administered by our hypothetical convert from Islam.) Let's say that this infant grows-up into adulthood, learns and practices the Muslim faith in near-total ignorance of his or her true Catholic identify, but lives a virtuous life nonetheless. After studying Islamic theology, this "Muslim" learns about an ecumenical conference with Catholics and decides to attend.
How should the Catholics present at the conference treat this "Muslim" participant? If he is in a state of grace, then he is fully Catholic; if not, then he is an apostate. In either case, he is definitively not a Muslim, at least according to Catholic dogma. In helping this person to be a "better Muslim," are the Catholics present helping him to become a "better Catholic" or a "better apostate"? If the latter, then they cannot be possibly helping him at all. If the former, then they should helping him to believe in the true Articles of the Faith. In either case, they could not be helping him to be a "better Muslim." They could only be "helping" him if they knew that he was, in fact, a true Muslim.