Travelling around an eternal circle

If travelling along the circumference of an eternal circle is the same as travelling in a straight line, then my question is this:

Does an infinite shape become finite when viewed in a higher dimension?

For example: An infinite two dimensional plane can host an infinite number of one dimensional lines, but can only host one infinite two dimensional plane. The latter makes it hard to see its shape because it is infinite. Likewise infinite three dimensional space can host an infinite amount of two dimensional planes and we can observe their shape, but only one eternal three dimensional space which makes it hard to know its shape.

So, can an eternal circle be a finite circle viewed from higher up, or an eternal sphere be a finite sphere from a higher dimension? Perhaps this is the reason we cannot fathom the shape of the universe. Is it really a finite sphere housed inside a higher dimension such as time? But residing in the sphere or circle makes us think we are travelling in a straight line because we cannot see the shape. When we head out into space, we are really going around a circle or sphere as observed from a higher dimension such at time, but from our perspective, we are traveling in a straight line.

Does infinite become finite as we step up to the next dimension?