What was outside the universe just after it formed?

Your speculation of universe is close to the truth as I have ever heard. Universe is as if a basket that being filled in by  energy, masses, space and time , then with out these four entities their would be no point of having universe . Mind you , since the time dimension of universe is having limited purposes , then universe is also having a limited size ,being as if place on surrounding space of unknown dimension. So how can any limited dimension can fathom the unlimited dimensions that is why the Intelligent Designer of both limitation and non-limitation of all dimensions ,then is the sole controller of all the created things , both inside and out side of the universe . How can we imagine of a soul of human being, which is immortal , being placed inside  a mortal body. This is the closes analogy of the limitation of universe being placed inside the unlimited space of the radiant of the Creator.

GOD WAS. Don't you kinow anything snowwie888? tsk!

It's easy to duck and dive around the basic thrust of your question ,but in reality , there are only two honest answers. 

Either the universe, when it formed, was the creation of existence itself  -- that there is no concept of existence ,either before or "outside" of our universe .

-- Or ,our "universe" formed within ,or from, a prior existing (infinite) universe -- at which point, the origin of the universe becomes the "it's turtles all the way down answer "

 That's like asking what's further north than north pole z

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Don't confuse the whole universe with the visible universe. 1 nanosec after the Big Bang, what is now the part of the universe we can see was a small sphere. There was lots more space beyond it. 

The center of your observable universe is where you are. You see 46 billion light years in all directions. But the entire universe has no center. 

You said if the entire universe has a size, it must have a perimeter boundary. This is not true. It could be finite but unbounded. The surface of the earth is finite, it has a size, a circumference and area, but no edge. 

There is no outside because the Universe is everything.

No, it doesn't "beg" that question. It raises or suggests that question. To "beg the question" means something entirely different from what you mean here. Look it up.

Let me emphasize what @Morningfox said. All ‘size’ descriptions relate to the OBSERVABLE universe. What is outside the observable universe is more universe - we are simply causally disconnected from it.

Every point in spacetime - assuming isotropic expansion - sees itself as the center of its observable universe.

All evidence point to the universe having zero curvature which implies an infinite universe. An infinite universe presents no problem to general relativity since it’s a change in the INTERNAL scale factor that IS the expansion of the universe.

As to what’s outside, again turning to general relativity, it does not require an outside to exist. General relativity refers to the 4 spacetime dimensions only - it completely describes the geometry of the universe with intrinsic geometry. No boundary or perimeter is required.

Since general relativity deals with intrinsic curvature it does leave open the possibility for different topologies (and extrinsic curvature) embedded in higher dimensions, and of course, there is the ever speculative “universe in a black hole” with the event horizon being an inescapable ‘boundary’.

The OBSERVABLE universe had a size and a perimeter, and that size and perimeter have grown.  As for the center, it's right in you. And me, and everybody else. We are each at the center of our own observable universe.

For the whole universe, it's probably infinite. At the very least, it is hundreds of times larger than the observable universe. There is no way to know, because by definition the observable universe is all we can ever see, or detect gravity waves from, or any other evidence from.

But based on what we can see at the edge of the OBSERVABLE universe, the rest of the universe has to be pretty much the same, out to hundreds of times the size of what we can see. Otherwise, galaxies near the edge of what we can see, would have different speeds and separations.

For all intents and purposes... we don't *know* what's beyond our universe.  There may be nothing;  there may be a 'parent' universe, there may be a multitude of other universes... but, there's nowhere we can point to that leads to 'outside' our universe.

Picture it this way... an ant is walking on the surface of a beach ball.  It's being blown up - so, the *surface* he's walking on is getting larger - but is there a center?  That 2-D surface is a representation of our 3-D universe - you can travel forever, and not come to an edge of any kind;  There's no 'perimeter' we'd be able to encounter. 

As for the 'center' of the universe - that works also with the beach ball... imagine it's going in reverse; the surface is getting smaller and smaller. Eventually, it's just a tiny, nearly dimensionless *point* in space.  The *whole universe* is in that point.  Then, it begins to expand... that expansion occurs everywhere, and more or less equally... that means that there's no single 'center' to that surface - or, if you wish, *everywhere* is the center... which means the center was where I am, *and* it's where you are.  Everywhere was in the center.