ETA: Although, that still doesn't seem to work -- your Estates miss the shuffle and so after T2 your deck is just 3 coppers, and you draw only 4 for your next hand, so is it possible to get Estate + Province in hand simultaneously?
Good point. After my original reply I successfully worked out that the deck had 3 Coppers, so thought that the shuffle had to put Estate and Province as the top two cards, i.e. I had forgotten the effect of the Borrow. Admittedly there are ways for a fifth card to be obtained, but they require another card (or cards) to be in the Kingdom.
One possibility is Lost City, with the opponent helpfully buying one at the right moment.
A second is Importer plus Band of Nomads (spend a favour for +1 card after buying the Province, thereby counteracting the -1 card token).
A third is Importer plus Cave Dwellers (spend favours to discard one or more cards to dig through to the missing Estate or Province).
A fourth is Importer plus City-State (with Province in hand, buy an Estate on T3 and spend favours to play it, but I don't think the Followers can then be played).
A fifth is Importer plus Desert Guides (spend a favour to discard the 4-card hand and draw five).
A sixth is Importer plus Fellowship of Scribes (shuffle Estate to top of the deck so that it's in the 4-card hand, play it, drawing Estate or Province, and then spend a favour to draw the necessary extra card, i.e. Province or Estate respectively).
A seventh is Importer plus Mountain Folk (spend five favours to draw three extra cards at the start of T3).
But the OP didn't mention any such combination as being part of the Kingdom.