There is a significant event in Israel's history that the author may have had in mind, based on his rhetorical question about escaping. Please turn with me to Ezekiel 17. This is about King Mattaniah, who was renamed Zedekiah.
This is about when Nebuchadnezzar took the upper echelons of the kingdom of Judah into captivity in Babylon. However, God granted a sort of salvation to a remnant of Judah: They were allowed to remain in the land, and Nebuchadnezzar installed Zedekiah as the king. A covenant was made, and Zedekiah was put under oath, such that he and the kingdom had to remain subservient. It could not be lifted up.
But instead of gratitude for the salvation that allowed the nation to continue, Zedekiah broke the agreement by trying to throw off the yoke. He had made a pledge to get through the immediate crisis because he really didn't have any other option, but after that crisis had passed, he tried to do his own thing. It seems he could not accept that God had him and the nation right where He wanted them because of their spiritual condition. Even though Zedekiah rebelled against Nebuchadnezzar, in reality, the rebellion was against God because Nebuchadnezzar was God's agent in this. But it was easier to agitate against the human representative than admit to, and deal with, the true reason for the circumstances.
God asks rhetorically in verse 15, Will he who does such things escape? Can he break a covenant and still be delivered? This was not even a covenant with God - it was an agreement between men. But God answers His own question in verse 18. He says, Since he despised the oath by breaking the covenant, and in fact gave his hand [meaning, in a pledge] and still did all these things, he shall not escape.
In this light, we can see some similarities between our lives and what is written in Hebrews. We have been given a salvation - one far greater than the one given to the remnant of Judah and the salvation given to the exodus generation. God offered a covenant to us, and it is the very best covenant that has ever been made available by God. We made a pledge at baptism. But the covenant requires absolute loyalty and subservience to God. Our lives are entirely in His hands because He paid for us. We owe Him everything. And the author asks rhetorically, How shall we escape if we neglect [or ignore] so great a salvation…?
God answers the question. The exodus generation who made the covenant at Sinai did not escape, and neither did the individual, Zedekiah, escape after going back on what he had agreed to. If we despise, neglect, or ignore the pledge we made, we also shall not escape. God says in verse 19 here that He will recompense, meaning inflict or repay on the person's head. Clearly, God takes these things very seriously, and we should as well.
But if we despise our oath by an illegal end-run around the constraints God places on us, we risk our salvation. Zedekiah went back on his pledge, and his salvation was taken away. His end was horrible. Israel likewise failed. So, the author asks rhetorically how we could possibly escape if we neglect an even greater salvation that is based on a superior covenant.