Your question has two flaws. (1) Justification is impossible and not desirable. (2) Occam's razor is a badly flawed standard.
Justification, showing an idea is true or probably true, is impossible. If you assess ideas using argument then the arguments have premises and rules of inference and the result of the argument may not be true (or probably true) if the premises and rules of inference are false. You might try to solve this by coming up with a new argument that proves the premises and rules of inference but then you have the same problem with those premises and rules of inference. You might say that some stuff is indubitably true (or probably true), and you can use that as a foundation. But that just means you have cut off a possible avenue of intellectual progress since the foundation can't be explained in terms of anything deeper. And in any case there is nothing that can fill that role. Sense experience won't work since you can misinterpret information from your sense organs, e.g. - optical illusions. Sense organs also fail to record lots of stuff that does exist, e.g. - neutrinos. Scientific instruments aren't infallible either since you can make mistakes in setting them up, in interpreting information from them and so on.
We don't create knowledge (useful or explanatory information) by showing stuff is true or probably true for reasons so how do we create knowledge? We can only create knowledge by finding mistakes in our current ideas and correcting them piecemeal. You notice a problem with your current ideas, propose solutions, criticise the solutions until only one is left and then find a new problem.
Occam's razor is problematic because it claims that you should not multiply entities beyond necessity without specifying what counts as necessity. As a result it has often been given bad interpretations like don't add stuff that isn't justified. It is sometimes true that a better explanation has been created by discarding an idea that people formerly thought was necessary, e.g. - Einstein discarding the ether in special relativity. Any idea should be judged by whether it solves problems that other ideas don't solve, regardless of the number of entities it invokes. For example, it is not a good objection to the atomic theory to claim that it assumes the existence of large numbers of atoms: that's a lot of assumptions ~10 the power 23 for any given object. You could say that's just one assumption but why count it as only one assumption? This is the sort of issue that comes up if you see the number of assumptions as the important issue.