$O(1)$ is love, $O(1)$ is life

$O(1)$ time is also called "constant time" but this term is a misnomer. $O(1)$ time doesn't imply that the runtime is constant, it implies that the runtime can be bounded above by a constant (mathematical definition), i.e., if $S$ is the set of all possible runtimes (in seconds) of the code, then,

$\text{Code is }O(1)\iff \exists k\in\Bbb{R^+}~\mid \sup(S)=k$

This means that the code need not have the same runtime for all possible inputs but that the set of all possible runtimes of the code for all inputs has a supremum (the supremum would be a positive real because runtime is always a positive real).

Consider the following code as an example (in Python 3):

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from time import sleep
n=int(input())
if n==1:
    sleep(30)
print("Hello world!")

For the above code, the intended inputs are integers. When the code is executed, if the input is n=1 , it waits for 30 seconds and then prints "Hello world!", otherwise it prints "Hello world!" straightaway.

So, assuming that printing happens in an instant, for integer inputs other than $1$ , the runtime is 0 secs (instant) but for n=1 , the runtime is 30 secs.

So, the runtime is bounded above by any $k\geq$ 30 secs, i.e., the supremum of the set of runtimes of the above code is 30, a constant, hence the code is $O(1)$ by definition.