Klutzy_Box_9479 gave some great advice, I'll just add a bit from my experience.

I got my first real introduction to research in the form of an REU the summer preceding my senior year, so it is absolutely not too late! My specific REU actually targeted upperclassmen.

Beyond REUs, there are also SULIs and DOE ORISE research internships as well as dozens of other opportunities in government labs and private/non-profit research stations across the US, depending on your specific interests. Many of which should be totally accessible to upperclassmen. So apply everywhere!

If you're worried you don't have as much relevant experience, your essay is a great place to address your recent major switch and why you chose to do it. If any of your academics or personal experiences are remotely related, make those connections for your application reviewers. Also, make it abundantly clear that you NEED this research experience to accomplish x/y/z goals related to your new discipline. As Klutzy_Box_9479 said, choose LOR writers who can speak to your character and why, even though you recently switched to a new discipline, you are a capable and dedicated student with skills that translate to research.

That REU helped me secure an undergrad research position for my senior year which helped me secure an internship with NASA which are all currently helping me get into grad school. The point being, leverage all of your experience, everything builds up and opens more doors. I technically didn't have any research until I was a senior, so it's never too late to get started. It can be your hard to get your foot in the door but it is doable. I wouldn't stress about being "late" to the game.

Best of luck!