According to Ancient Greek and Latin sources, several Egyptian pharaohs had made attempts to connect the Nile to the Red Sea in the past, but it was only accomplished under the Persian King, Darius the Great around 500 BCE. Even then, several of the same sources dispute that claim. Depending on how you specific you want to be, this was the same as digging the Suez Canal.

In the Histories, Herodotus claims that Darius completed a canal connecting the Nile to the Red Sea, and that it was large enough for two trireme warships to sail through it side by side. He also says that this canal was started in the reign of Pharaoh Necho II, a century earlier, but abandoned because the arduous work of digging a canal through the Sinai desert killed too many workers. In a rare case of Greek and Persian synchronicity, an inscription from Darius the Great found near Suez actually backs up this story. It reads:

King Darius says: I am a Persian; setting out from Persia, I conquered Egypt. I ordered to dig this canal from the river that is called Nile and flows in Egypt, to the sea that begins in Persia. Therefore, when this canal had been dug as I had ordered, ships went from Egypt through this canal to Persia, as I had intended.

Based on the location of that Persian monument, and Herodotus' description, Darius' canal exited into the Red Sea very close to Suez, where the modern canal opens as well. However, both Herodotus and the Persian inscription also make it clear that it didn't cut north to connect with the Mediterranean. Instead, the design of this canal reflected Egyptian priorities and connected directly to the Nile Delta. Of course, ships could then navigate the Delta and get into the Mediterranean, but it was not as direct. Whether you want that to count as digging "the Suez Canal" proper, is up to you.

However, several later Greek and Latin authors all said that the canal did not connect the Nile to the Red Sea, and was thus incomplete. One of those authors, Diodorus Siculus, even definitively states that the canal was only completed in the time of King Ptolemy II, 250 years after Darius' time. So historians argue that Herodotus was simply incorrect and add it to a long list of his inaccuracies. However, Darius' Suez Inscription supports Herodotus' claim, and would be a weird thing for Darius to lie about in an official monument. The more likely explanation is actually reflected in a series of later historical reports.

Diodorus Siculus' story of Ptolemy II "completing" the canal emphasizes that it could only be done after Ptolemy's engineers invented a water lock to prevent salt water flowing into the Nile Delta from the Red Sea and the large salt lakes that the canal passed through. It's entirely possible that Darius' canal had to be partially sealed off after people realized that it was inadvertently ruining the water supply of the eastern Delta. That wouldn't necessarily have cut off shipping, since only small buffers would be needed between the main canal and the Greater Bitter Lake. If needed, ships could be dragged overland or cargo could be transferred to a new vessel.

The other possibility, with lots of later historical evidence, is simply that lack of maintenance allowed the canal to become blocked up with silt. In the 2nd Century CE, the Roman-Egyptian geographer Claudius Ptolemy referred to an active canal between the Nile and the Red Sea as the "River of Trajan." That naturally raises a question of how a canal previously connected to Darius I and Ptolemy II ended up named after Trajan. In all likelihood, Trajan too oversaw the "completion" or re-opening of the same basic canal. 400 years later, the canal still existed, but was apparently silted closed once again when the Arabs conquered Egypt from the Romans in 641. It was apparently reopened one last time early in the Arab occupation of Egypt, but ultimately was not maintained and allowed to silt shut permanently some time after the mid-8th Century.

Based on the series of names associated with the canal, the centuries in between each of them, and contemporary authors' apparent lack of knowledge of previous canals, the ancient Suez Canal just didn't work very well. It seems to have filled with silt too quickly to be used for extended periods of time without constant maintenance, and was probably not worth the effort it took to maintain if Egypt wasn't already prospering.

Edit: There was also a very brief revival under Fatimid Caliph Al-Hakim bi-Amr Allah around 1000 CE, but it resilted almost immediately.