Is it possible to play without time limit?

According to Wargamer's review of ICBM, you can change the length of the timer in the pre-game config, to make it longer or shorter.

This is due to the game’s scoring system which is based around inflicting as many casualties as possible on your opponents, within an artificial time limit—one that is triggered when the world’s pollution levels (produced by nuclear fallout), reaches a certain percentage. Both the percentage of pollution needed to trigger the countdown timer and the length of the timer itself can be changed in the pre-game configuration settings.

However, as far as I can tell, there's no vanilla way to completely remove the time limit or play in a "kill all enemies" game mode without the use of custom mods or other tools. The only possible game modes are the ones given to you with the built-in time limits.