This meme was first started by TheTentor, a member of video-sharing website YouTube who later closed his account. Gottam is simply a part of “Gotta Move That Gear Up!” - a phrase that a playable character named the Engineer in video game Team Fortress 2 uses as a voice command. If you do some splicing you’ll get gottam. Gottam is usually a phrase that the Vagineer uses, which is a different meme created by J16FOX. People started to spam this voice command just like The saying “NEED A DISPENSER HERE” and the heavy saying “Pootis Spenser Heare!” both other separate memes. Thetentor later made a new account, thestolken, in which he has re-created the gottam on his account. Gottam was also the first Team Fortress 2 meme to ever be .
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Example from official Wiki: