A military invasion would be kind of redundant at this point since we're already invading with propaganda. This is why Don Jr was there. Think about it...
Just to get a feel for the scale of this endeavor... There are 57K-58K people in Greenland, that's it. Getting the vast majority to be into Trump and MAGA is a way, way easier investment than investing to get the popular vote in the US. If Trump/Musk spent $1B, they could split that up into $20K per person to buy them off...and they could do that from their personal funds. If, instead, they used tax payer dollars, they could get approval to spend $1T and hand over $20M per person or spend $20M on propaganda per person in Greenland. They probably don't even need to spend that much money since Musk can inundate them with pro-US posts through twitter algorithms. All there needs to be is some kind of option of putting it to a vote, then a few corruptible or misinformed souls and BINGO!