Is it guaranteed that all possible random numbers can be produced? As far as I know PRGs get an input (seed) and generate a larger output value than the input. Therefore is it possible that some outputs will never be generated? based on the fact that input is smaller than the output.
PRGs get an input (seed) and generates a larger output value than the input.

Indeed. The standard definition of a PRG makes it a deterministic polynomial-time algorithm with input a seed in $\{0,1\}^n$ and output in $\{0,1\}^{\ell(n)}$ with $\forall n, \ell(n)&gt;n$; and an other characteristic (pseudorandomness).

is it possible that some outputs will never be generated?

It's not only possible, it's certain, for all $n$. To prove this, we only need to count the possible inputs: there are $2^n$; and the number of outputs: there are $2^{\ell(n)}$. The condition $\ell(n)&gt;n\ge 0$ implies $2^{\ell(n)}&gt;2^n$. And since the algorithm is deterministic, there can't be more possible outputs than possible inputs.


Is it guaranteed that all possible random numbers can be produced?

Also yes, but in another sense.
If we truncate the output into $\lfloor\ell(n)/k\rfloor$ bitstring of $k$ bits, then it becomes possible that each one of the $2^k$ potential output bitstrings of $k$ bits is reached for some input when $n$ grows high enough. In fact, pseudorandomness implies that holds¹. Every possible output of any fixed size $k$ bit is reached¹ for large‑enough $n$ and when we consider all the $2^n$ possible inputs.
Now we only need to choose $k$ such that all the random numbers thought are in $[0,2^k)$, and then all possible random numbers thought are¹ produced.

¹ except perhaps for vanishingly few $n$