Is there a need for $L\subseteq \Sigma^*$ to be infinite to be undecidable?

I mean what if we choose a language $L'$ be a bounded finite version of $L\subseteq \Sigma^*$, that is $|L'|\leq N$, ($N \in \mathbb{N}$), with $L' \subset L$. Is it possible for $L'$ to be an undecidable language?

I see that there is a problem of "How to choose the $N$ words that $\in$ $L' "$ for which we have to establish a rule for choosing which would be the first $N$ elements of $L'$, a kind of "finite" Kleene star operation. The aim is to find undecidability language without needing an infinite set, but I can't see it.

Is there a need for $L\subseteq \Sigma^*$ to be infinite to be undecidable?

I mean what if we choose a language $L'$ be a bounded finite version of $L\subseteq \Sigma^*$, that is $|L'|\leq N$, ($N \in \mathbb{N}$), with $L' \subset L$. Is it possible for $L'$ to be an undecidable language?

I see that there is a problem of "How to choose the $N$ words that $\in$ $L' "$ for which we have to establish a rule for choosing which would be the first $N$ elements of $L'$, a kind of "finite" Kleene star operation. The aim is to find undecidability language without needing an infinite set, but I can't see it.

EDIT Note:

Although I chose an answer, many answers and all comments are important.

Knowing that there is no surjection from $S$ to $\mathcal{P}(S)$.

Is there a need for L to be infinite to be undecidable, i.e. $L\subseteq \Sigma^*$?

I mean what if we choose a language $L'$ be a bounded finite version of $L\subseteq \Sigma^*$,

 $|L'|\leq N$, ($N \in \mathbb{N}$), with $L' \subset L$ , Is it possible for $L'$ to be an undecidable language?

I see there here is a problem of "How to choose the $N$ words that $\in$ $L' "$ for which we have to stablish a rule for choosing which would be the first $N$ elements of $L'$, a kind of "finite" Kleene star operation..The aim is to find undecidability language without needing an infinite set, but I can't see it.

Is there a need for $L\subseteq \Sigma^*$ to be infinite to be undecidable?

I mean what if we choose a language $L'$ be a bounded finite version of $L\subseteq \Sigma^*$, that is $|L'|\leq N$, ($N \in \mathbb{N}$), with $L' \subset L$. Is it possible for $L'$ to be an undecidable language?

I see that there is a problem of "How to choose the $N$ words that $\in$ $L' "$ for which we have to establish a rule for choosing which would be the first $N$ elements of $L'$, a kind of "finite" Kleene star operation. The aim is to find undecidability language without needing an infinite set, but I can't see it.