<p><a href="https://i.stack.imgur.com/qNWsZ.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/qNWsZ.png" alt="extruded text on flat surface"></a></p>

<p>Hey!</p>

<p>Pretty new to all this. Wondering how you would approach this problem to have an extruded element on top of a flat surface. I want to avoid lots of support material (actually no support at all for a cleaner print and no work with sanding etc.) I intend to print this inverted in Z (i.e. text down) for the main structure.</p>

<p>My only idea would be to print it separately and then glue it on. But maybe there is another solution that comes to your mind?</p>

<p>Cheers!</p>

Supporting the text while printing should simply not be a problem, if printed in the orientation shown. The text, as per your description and shown in the illustration is extruded vertically and there is no overhang. No support should be needed at all.
A few notes:
The bottom (dark grey) portion of your object does have a significant overhang, and may need some support depending on the specific shape. But support for that should not be near the text or affect it.
Text can be tricky to print with high quality if the width is not much bigger than your nozzle size. This is not specific to text, but rather feature size, slicer settings, and printer/filament capabilities. Experimentation is your friend - print it, and then address any quality problems that you find.
If you want the text to be a different color (as in your illustration), you might be in luck. There is a technique to pause the printer at desired layer height, swap out the filament, and resume printing. Your shape would lend itself to this technique. It's not too hard, but the specifics do depend on the software and printer you are using. There are quite a few good writeups on various 3D printing sites. If you want to ask about this, please ask another question, with this information.