Sources connected to the launch tell TMZ ... SKIMS pushed $2 million in product within the first few minutes of Kim's campaign going live Tuesday, and nearly every piece of inventory sold out in lightning speed.

Our sources say the first-day sales numbers are unprecedented for shapewear and undergarment brands. How's this for context ... in its first YEAR on the market, Spanx made $4 million in profits ... and SKIMS made half that amount in only a couple hundred seconds.

In a scene straight outta Black Friday, there was a mad dash to scoop up Kim's newest release ... there was so much traffic on the website before the products even went on sale, the site crashed and SKIMS had to delay the launch for an hour.

We're told SKIMS had thousands of items up for sale Tuesday. Nothing was priced north of $100 ... and after selling out the inventory, Kim's team began working feverishly to restock and produce more products to get to consumers ASAP.

The goal for Kim and SKIMS ... for everything to be readily accessible for everyone to wear.

Kim launched a massive social media ad campaign for the rollout, even bringing in Alice Marie Johnson, the woman KKW helped free from prison, to push and model the product.