After sin entered the world in the Garden, there were consequences. But God already had a plan to deal with sin and bring us back into a relationship with Him. (That plan being Jesus.)
Throughout the Bible, we see God’s love towards His people.

Genesis 12: Sarah and Abraham go to Egypt due to a famine in Canaan (where they lived).
Abraham introduced Sarah as his sister, fearing he might be killed so another man could take Sarah as his wife.
Pharaoh ends up taking an interest in Sarah as a potential wife, bringing her into his household.
But then God strikes plagues upon Pharaoh's household; Pharaoh realizes who Sarah is; and she is given back to Abraham.

Note: After this happens, in the beginning of Genesis 12, God tells Abraham that He is going to make him and his descendants into a great nation!
And - Abraham plays this game again (of having Sarah act as his sister) in Genesis 20!

There are many instances of God protecting, blessing, and loving His people. Broken, sinful, and in-process though they were.

Grace is defined as “undeserved favor.” Or, to put it more simply, it’s when we receive something that we don’t deserve.
The biggest example of this is Jesus dying on the cross. Man caused sin to enter the world - not God.
But God, in His goodness, sent Jesus to be the ultimate sacrifice in our stead.
There are many instances throughout the Bible where God gives favor to His people, despite who they are, because they are His. Because of who He is - not who they are.

Mercy can be seen almost like the opposite of grace. Mercy is when God withholds what we do deserve.
Again, the biggest example of this is Jesus. We deserve death; to be eternally separated from God due to our sin; and to be fully left with the consequences of our sin. But God, in His mercy, hasn’t left us to that fate.
He was both gracious and merciful by sending Jesus to die in our place.