That was always an option from the EU's point of view. It wasn't an option for Theresa May because of what she decided her red lines were.
Imagine for a second that Northern Ireland was not part of the UK.
Without Northern Ireland, the Brexit options on the table would have been the following:
Soft Brexit
Hard Brexit
Soft Brexit means more or less full access to the single market and customs union, more or less full adherence to EU law in all areas affecting trade, continued free movement of goods, services, people and capital. This is the Norway model or to a lesser extent the Swiss model. This would be an interesting option for a Europe-adjacent country which does not wish to join the Euro. It was not particularly interesting for the UK because we had a legally binding opt out from ever joining the euro.
Hard Brexit means basically none of the above as your starting point, and you negotiate a free trade deal as any other non EU country would with better access to the single market the more rules you are willing to accept, and less good access to the single market the fewer rules you are willing to accept.
Those are the two options, everything else is window dressing.
What complicated matters with Brexit is that Northern Ireland is part of the UK. The Good Friday Agreement requires there to be an open border between Ireland and Northern Ireland, and EU law requires there to be a hard border between countries inside the SM/CU and countries outside of it. There was never any way of squaring that circle that wasn't going to be a horrible bodge job.
It is a problem from a democratic point of view. Ireland and the UK both joined the EU at the same time, so we were both outside the EU with our common travel area beforehand, and then we were both inside the EU with our common travel area afterwards. Brexit was the first time in history that one of us has been inside the EU and the other has been outside it, so it was completely uncharted territory.
That meant that for the UK, the options really on the table were Soft Brexit or Complicated Crap Version of Hard Brexit Which Pleases No One.
People did raise this as a potential issue before the referendum but it was dismissed as Project Fear.
The timing of triggering Article 50 made no difference because the options on the table never changed at any point in the negotiations.