I've invented a setup to get the most optimal round 1 possible. This optimization eliminates the cursor obscuring that the game naturally does when it's not your turn. Here's how it goes:

1. Press the windows key on your keyboard. Doing this allows you to see your mouse.

2. As the shotgun rounds are revealed, line up your cursor with the top left corner of the gold part of the second round from the left. This will have your mouse lined up with the shotgun.

3. Spam click the spot where you lined up until shotgun appears. Shoot yourself with a blank. Use muscle memory to bring the mouse back up to its original spot. Shoot yourself again with a blank. Repeat muscle memory return and then shoot the dealer.

4. Load 2 do the same mouse cursor setup. Spam, then shoot the dealer.

The fastest round 1 I've gotten is 57 seconds when I shot the dealer. Hope this helps!