Because of a reason vs for a reason

"Everything happens for a reason" is a saying that implies predetermination, and fatalism. However, the preposition for doesn't necessarily imply a future. It's the connotation behind the saying that implies that an end will have happened because it was fated to.

If you're not a fatalist, and this isn't what you intend to convey, you could say that everything is connected, and every effect must, then, have (or have had) a preceding cause.

In the adage

Everything happens for a reason

the verb is in the present tense. This is sometimes called the enduring present, and it indicates the truth of a general proposition. Things have happened for a reason in the past, they happen for a reason now, and they will continue to do so in the future. Mathematics provides the simplest examples:

Eight plus four equals 12.

The implied meaning of the saying goes beyond the law of cause and effect (i.e., every effect has a definite cause). It means that every situation is part of some comprehensible plan, even if we are unable to discern what that plan is.

Because of licenses an explanation as its object, so taken literally, "because of a reason" is redundant. It's saying "because of a thing that's the cause." You might be better off with a phrasing of the law mentioned above.