From my understanding the “disgusting thing” appears either just prior to or at the beginning if the Great Tribulation, see Matthew 24:15-22: “Therefore, when you catch sight of the disgusting thing that causes desolation, as spoken about by Daniel the prophet, standing in a holy place (let the reader use discernment), then let those in Ju·deʹa begin fleeing to the mountains. Let the man on the housetop not come down to take the goods out of his house, and let the man in the field not return to pick up his outer garment. Woe to the pregnant women and those nursing a baby in those days! Keep praying that your flight may not occur in wintertime nor on the Sabbath day; for then there will be great tribulation such as has not occurred since the world’s beginning until now, no, nor will occur again. In fact, unless those days were cut short, no flesh would be saved; but on account of the chosen ones those days will be cut short.”
However, the mark of the beast will be issued by the 8th King/beast, which won’t appear until the 7 headed beast of Revelation 13 gets its mortal wound that is then healed. The appearance of the 8th King/wild beath happens after the Great Tribulation is cut short, according to how I read Revelation 13. The way I understand it, this is the period of the 42 months when people will have to choose God’s Kingdom or Satan’s rulership as expressed through the 8th King/wild beast.