From Haaretz:

There are a number of very interesting points in the assessment. It combines both painstaking summaries of the open-source intelligence on the attack – reports and videos made by local Syrian civilians which were posted on social media and reports from international organizations and NGOs – along with the declassified results of U.S. intelligence gathering, confirming and adding new details. This includes both signal intelligence and geospatial intelligence. The available information, along with the timing of the strike, reports on the ground from the affected area, the identity of the Syrian aircraft and personnel involved and the medical details of the casualties, leave no doubt that this was a sarin attack launched by the Assad regime.

The White House naturally didn't divulge many details of its own intelligence gathering. However, one quote from the briefing regarding the bombs carried by a Syrian Sukhoi Su-22 bomber is particularly revealing: "We have one particular munition that we've seen via overhead that we think is a munition that contains sarin." In other words, American intelligence claims to have footage, either from a satellite or a reconnaissance aircraft of the Syrian plane it believes carried out the attack being loaded with a bomb containing sarin. That indicates an intelligence or military service, either of the U.S. or an allied nation, had been intensely surveilling the Shayrat airbase even before the chemical attack.