"Possible", "necessary" and "real" are the three modes of existence in ontologies with possible words. One of the main possible-worlds models has been introduced by Leibniz. But even in these ontologies, "possible" does not imply "necessary". Instead: "Possible" is defined as "real in at least one world". While "necessary" means "real in all worlds".

I would not complicate the original question with the concept of infinite time. At least, the concept of infinite time opens up new questions ...

"Possible", "necessary" and "real" are the three modes of existence in ontologies with possible worlds. One of the main possible-worlds models has been introduced by Leibniz. But even in these ontologies, "possible" does not imply "necessary". Instead: "Possible" is defined as "real in at least one world". While "necessary" means "real in all worlds".

I would not complicate the original question with the concept of infinite time. At least, the concept of infinite time opens up new questions ...