It wasn't impossible, was it? Johnson has proven that.
She used the same tactic as Boris Johnson by calling an election to try and get a big majority which could implement the referendum in the face of opposition parties who had voted for it but now refused to actually abide by it. She was such a poor politician she instead lost her majority and ended up in a limbo controlled by her opponents. She had a party filled with MPs who openly lied to the voters during her disastrous GE campaign, saying they'd implement the Brexit vote and then immediately turning around and doing everything they could to stop it once elected. She did nothing to get a grip on her party and just drifted, completely lost and weak.
Then Boris Johnson stepped up.
1. He won the party leadership.
2. He kicked out a huge number of MPs (>40?) that had openly betrayed the voters, in some cases by switching after being elected to a party with the exact opposite of the policies they ran on. This plunged him deep into minority territory.
3. Parliament was filled with MPs who knew they'd lose the moment an election occurred due to those betrayals, and thus for the first time in history Johnson was faced with an opposition that kept voting against a chance to take power - the entire reason for their existence! Yet he still managed to get another general election.
4. He forced all of his prospective MPs to take a public oath that they'd actually implement what they said they'd implement in the party manifesto this time. He flushed out huge numbers of them that were untrustworthy.
5. He ran a strong campaign that gave him a huge majority.
6. He filled the cabinet with people who were committed to "getting brexit done" as he put it. He brought in a notoriously tough advisor who has already supposedly squashed multiple plots to reverse the referendum.
7. He replaced the Brexit negotiator with someone who is actually interested in negotiating and who believed in British independence, vs Theresa May's picks who didn't.
Except for the first step these are all things Theresa May could have done but was too weak or politically un-astute to do. Hardly impossible, it just required political strength and leadership.