This isn't exactly true for most beginners. 15 years of practicing off and on, here is what I learned.

You'll likely go a while before noticing at first. After practicing a bit it will feel like you've gotten worse because you are having more thought interruptions.

This is an illusion. You aren't having more thought interruptions, you're getting better at noticing them. The "goal" is the skill of noticing and refocusing not the time between thoughts. As you continue to practice the time between thoughts will increase naturally but you can't work on that directly the same way you can't force yourself to have an insight by thinking harder.

Eventually you can move away from dedicated practice time toward practicing all the time in your daily activities. You will find if you go deep enough that you have been practicing the skill of entering a "flow" state.

One thing to keep in mind is that the western concept of meditation with the religion removed is marketed to you heavily by corporations as a tool for improving focus, mental clarity, and productivity. It can do those things. They market it because they want you to meditate on your time so you work harder for them with less burnout. Please don't meditate so you can be a better wage and tax slave. Please don't skip this valuable practice because someone else wants to use it against you. Meditate for yourself. Use any gains you achieve in life to turn towards building a better you in other ways.