You won't have scores of theorems in your introduction, so a soft approach could be
\documentclass{article}
\usepackage{amsthm}
\newtheorem{thm}{Theorem}[section]
\newtheorem{lem}[thm]{Lemma}
\newtheorem*{thm*}{Theorem}
\begin{document}
\section*{Introduction}
In this paper we'll prove the following result.
\begin{thm*}
All numbers are odd.
\end{thm*}
This striking result has several consequences.
\section{Preliminary results}
Here is the most useful lemma.
\begin{lem}
The number $1$ is even.
\end{lem}
\begin{proof}
Everybody can see it.
\end{proof}
Here is a first consequence.
\begin{thm}
All prime numbers are odd.
\end{thm}
\begin{proof}
Since $2=1+1$, $2$ is odd.
\end{proof}
\section{The main result}
We are now ready to prove our main result.
\begin{thm}
All numbers are odd.
\end{thm}
\begin{proof}
Since $0$ is obviously even, $1$ is odd. But $1$ is even, so also
$0$ is odd. A number $n>1$ is a product of primes, hence odd.
\end{proof}
\end{document}

Alternatively, you can define a generic environment for theorems in the introduction:
\newcommand{\introthmname}{}
\newtheorem*{introthminn}{\introthmname}
\newenvironment{introthm}[1]
{\renewcommand{\introthmname}{#1}\begin{introthminn}}
{\end{introthminn}}
and then state your theorems in the introduction as
\begin{introthm}{Lemma}
The number $1$ is even.
\end{introthm}
\begin{introthm}{Theorem}
All numbers are odd.
\end{introthm}
Here's a version that numbers the statements in the introduction and also swaps the numbers.
\documentclass{article}
\usepackage{amsthm}
\newtheorem{thm}{Theorem}[section]
\newtheorem{lem}[thm]{Lemma}
\newcommand{\introthmname}{}
\newtheorem{introthminn}{\introthmname}
\newenvironment{introthm}[1]
{\renewcommand{\introthmname}{#1}\begin{introthminn}}
{\end{introthminn}}
\swapnumbers
\begin{document}
\section*{Introduction}
In this paper we'll prove the following result.
\begin{introthm}{Theorem}\label{thm:main}
All numbers are odd.
\end{introthm}
This striking result has several consequences.
\section{Preliminary results}
Here's the most useful lemma.
\begin{lem}
The number $1$ is even.
\end{lem}
\begin{proof}
Everybody can see it.
\end{proof}
Here's a first consequence.
\begin{thm}
All prime numbers are odd.
\end{thm}
\begin{proof}
Since $2=1+1$, $2$ is odd.
\end{proof}
\section{The main result}
We are now ready to prove our main result, already stated as
Theorem~\ref{thm:main} in the introduction.
\begin{thm}
All numbers are odd.
\end{thm}
\begin{proof}
Since $0$ is obviously even, $1$ is odd. But $1$ is even, so also
$0$ is odd. A number $n>1$ is a product of primes, hence odd.
\end{proof}
\end{document}

\documentclass{...}
and ending with\end{document}
.