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Epson iPrint App requires just a WiFi connection of your Android device with your WiFi printer.
Your WF-3620 printer is listed as being compatible, not with iPrint, but as being compatible with
Google Cloud printing
A link to Epson Connect is here:
Please try the Epson Connect app. See if it works for you, I suggest. At very least, if it does, it proves that nothing is wrong with your printer... which is still possible at this point.