In 2018 I was basically spending every cent I pulled in and hating it. That same year I decided to try to start saving. I did basically what you suggest, only every paycheque I'd move whatever remained from my last paycheque into savings. Usually, that was like 100 bucks or so, and now and then I had to steal from it for various reasons... but by 2020 the savings account was a respectable 15,000 or so.
So, my wife and I bought a house, which destroyed my savings but even with the extra expense of homeownership, I'm already stashing into savings, building my crypto portfolio, and planning future investments.
It really doesn't take long to get the ball rolling if you just start with even 100 a month!
Really happy for you and thank you for sharing. It's inspiring!