Should we be bragging on God? Yes, of course! God tells us to boast in Him:
This is what the LORD says: “Let not the wise man boast of his wisdom or the strong man boast of his strength or the rich man boast of his riches, but let him who boasts boast about this: that he understands and knows me, that I am the LORD, who exercises kindness, justice and righteousness on earth, for in these I delight,” declares the LORD.
We worship God because He is so good to us. His faithfulness is the same to every generation. In fact, He is so amazing and so good, it is hard not to worship Him.