What You're Seeing Right Now
Those little yellow clusters are the flowers of the sycamore (Acer pseudoplatanus), and at this stage they are purely the flowering parts of the tree doing their pollination work. They have no seeding potential in themselves and will simply break down into the compost over time if left, adding a small amount of organic matter to your beds in the process. So no, you are not about to accidentally grow a sycamore forest from this particular shower of yellow fluff.
What Sycamore Seeds Actually Look Like
The seeds are a very different thing entirely and you'll know them when you see them. Sycamore seeds come in pairs joined together and each seed has a distinctive papery wing attached to it, forming that characteristic helicopter or propeller shape that spins as it falls from the tree. They are sometimes called samaras or, more affectionately, helicopters or spinning jennies. They are considerably larger than the flowers currently covering your beds and completely unmistakable once you've seen them. These winged seeds typically fall from late summer through to autumn, so you have several months before that becomes something to think about.
When to Act and How
When the helicopters do start arriving later in the season, that is the point to be vigilant, particularly in your raised beds where the loose, rich compost gives sycamore seedlings exactly the conditions they love to germinate in. The window between seed landing and seedling emerging can be surprisingly short in warm weather, so a quick weekly check and weed of your beds through late summer and autumn will catch them before they get established.
The easiest time to remove sycamore seedlings is when they are very young, at the seed leaf stage, when the root system is minimal and they pull out cleanly with almost no effort. Leave them a few more weeks and you'll find they develop a surprisingly tenacious root for such a young plant, particularly if the taproot has had a chance to get down into your compost.
An oscillating hoe is genuinely one of the best tools for this job. Rather than pulling seedlings out by hand one by one, a good oscillating hoe, (This page contains affiliate links for products I use and love. If you take action (i.e. subscribe, make a purchase) after clicking a link, I may earn some gardening commission, which helps me keep the Garden Ninja Blog free for all.
Sometimes called a stirrup hoe or hula hoe, cuts through seedlings just below the soil surface on both the push and pull stroke, making light work of a bed full of young weed seedlings in a fraction of the time. The blade works with a back and forth motion that severs the roots cleanly without disturbing the soil too much, which also avoids bringing buried seeds up to the surface where they'd germinate.
It's a tool I use constantly through the growing season and it makes a real difference to how quickly you can keep on top of things.

Little and often is the approach that keeps sycamore seedlings manageable. A five-minute pass with the hoe every week or two through late summer and autumn will keep your beds clear with minimal effort compared to letting them get established.
A covering of fine mesh or fleece over your beds during the main seed fall period in autumn can also intercept a lot of them before they reach the soil surface, which is worth considering, given how many trees you have backing onto the garden.
For now though, enjoy the spring growth and don't worry about the yellow flowers. Your raised beds are safe for the time being.
Lee Garden Ninja