"Lift the nose of the umbrella upward with a thin rigid object such as a ruler, coat hanger, or fossilised cat penis," one Twitter user helpfully suggested.
"Have you tried turning it off and on?" another asked, while another quipped the conundrum would make "the ultimate job interview question at Google".
"Better hurry, 28 more days and the umbrella gains squatters rights," another added.
While the name of Mr Ponticelli's company has not been revealed, it is understood it operates out of a US office run by WeWork, an American real estate firm that provides shared workspaces for technology start-ups.
Mr Ponticelli told Vice he arrived at work on Monday morning to discover the freak accident, describing it as a "does not compute moment".
"Sometimes you've got a problem and you see a clear solution. Sometimes you see a problem, and you know the solution will be messy, but there's still a solution," he explained.
"There was no solution here. The seal was perfect. An umbrella had the door locked perfectly."
Initially, the four co-workers stood around the locked door for half an hour, repeatedly jiggling the door in an attempt to dislodge the brolly.
"It was geometrically perfect, how the umbrella had fallen. The door would not budge," Mr Ponticelli told Vice.
"We tried coat hangers, we tried our fingers, we tried wedging it, we tried picking it up.
"The windows on the outside overlook a roof on a nearby office, but there was no latch. They're just big panes of glass."
Eventually, they contacted WeWork, who provided an alternative space in another empty office as the problem was investigated.
The following morning, Mr Ponticelli took an arsenal of extra tools with him, including "a screwdriver, a pair of pliers, extra coat hangers" — but nothing worked.
WeWork then hired an engineer who "specialised in getting in closed offices" to fix the situation, but they also failed.
That person suggested they hire a "super engineer" — although they wouldn't be available for days and would cost a small fortune.
Eventually, on Tuesday night, someone cracked and cut a small hole in the ceiling and used a piece of wire to move the umbrella out of the way.
Mr Ponticelli told Vice he had no idea how the umbrella fell in that precise way.
"My theory is that the maintenance crew, who came in on Friday evening … something happened that caused the umbrella to fall in such a way that could never be replicated in 1000 years," he said.
It was a sentiment he echoed in another interview with BuzzFeed News.
"In a thousand years, you'd not be able to replicate this," he said.
"The umbrella has turned our office into, essentially, an unmanned panic room with no way in."