For the longest time I couldn't figure out how to get first layers with invisible extrusion lines like how they are on the Prusa factory printed LCD covers. I don't know if this is how they do it, but this is what worked for me and hopefully this guide will help you achieve perfect first layers. The key: print your first layer very, very slowly.
Guide:
Set your first layer speed to 10mm/s and first layer acceleration to 500mm/s^2. I also used a first layer extrusion width of 0.5mm with 0.4mm nozzle and a first layer height of 0.2mm.
Print the sample square and keep reprinting with a slightly lower offset each time in increments of 5μm (0.005mm) until you cannot recognize the pattern of the extrusion lines. If you go any lower than this you will start to see the pattern again.
That's it! You're done.
Tips:
Material choice is important. PLA is difficult to get this effect with. I have found success with PETG, Nylon & PC.
Textured beds are your friend. I have gotten invisible lines on a satin sheet, but only for a limited material selection. It doesn't do as good of a job of welding the lines together. A smooth sheet has this disadvantage to an even greater extent.
Higher first layer temps and bed temps may help. I did not have to resort to this though.
I included a file for a full-bed sheet that fits on Prusa dimensioned beds. If you use a Prusa printer older than a MK4, use this guide (Bed Level Correction) to ensure that you have an even offset across your whole bed. Similar guides exist for other printers that don't use nozzle probing for establishing first layer offsets.