The assurance of the promise

God makes promises to Abraham and they still stand today, we know this. But sometimes we can doubt the security of the promise, after all it's not exactly like a legal contract we have with our employer or anything.

The writer to the Hebrews explains why we can hold God to his contract:
When God made his promise to Abraham, since there was no one greater for him to swear by, he swore by himself, 14 saying, “I will surely bless you and give you many descendants.” 15 And so after waiting patiently, Abraham received what was promised. (Hebrews 6:13-15 NIV)
The basic way a covenant worked in the Bible was that you would swear by something greater than yourself, hence why people swear by God, the implication is that whatever you swore by would hold you accountable, it's almost like a co-signer or collateral. In God's case there is nothing for him to swear by because nothing is greater than him so he just makes the promise, and we know he's faithful because he did it.

God still follows the law at the time, but because of the abstractness of God he does it in his own way as the writer explains:
People swear by someone greater than themselves, and the oath confirms what is said and puts an end to all argument. 17 Because God wanted to make the unchanging nature of his purpose very clear to the heirs of what was promised, he confirmed it with an oath. 18 God did this so that, by two unchangeable things in which it is impossible for God to lie, we who have fled to take hold of the hope set before us may be greatly encouraged. (Hebrews 6:16-18 NIV)
God bound himself by his own oath, he would call himself to account, and we see this time and time again throughout the Old Testament as he goes back to the promise that he made reminding himself that he is bound to it.

God worked through the cultural constructs at the time so there could be no argument. God has made a promise and he will be faithful to it!