There isn't really an "inside of". There is no other universe that our universe is expanding into. The universe itself just "is", it is made of space-time and that metric is expanding and accelerating. Why it exists is philosophy. Maybe it was made just for us to exist in. Maybe it doesn't give a shit about us and we're simply hydrogen left to own devices long enough to futilely question its own existence.
When we talk about the universe we're rarely talking about what do not know yet, but rather what is possible to know.
Whether there is another universe "outside" of ours is not just something we don't know. It's something we cannot know but it's also something that cannot matter. The observable universe is, by definition, the total encompassment of everything that can possibly ever matter to us in even the strictest mathematical sense.
When we talk about the universe we're rarely talking about what do not know yet, but rather what is possible to know.
Whether there is another universe "outside" of ours is not just something we don't know. It's something we cannot know but it's also something that cannot matter. The observable universe is, by definition, the total encompassment of everything that can possibly ever matter to us in even the strictest mathematical sense.