How to teach sympathy/empathy in Buddhism?

I have been following Buddhism and mindfulness for a while now. I have a 5 year old son and want to teach him to be sympathetic/empathetic and grateful but im struggle to reconcile some of the Buddhist ideals. In my understanding, Buddhism teaches that we should be thankful for exactly the things we have (not to desire more/less) but to trust in the unfolding of our life. This is easy to say since I was lucky enough to be born into a productive family and am living a mostly positive life, etc. But when I look at the less fortunate people, homeless, poor, addicted, etc., I struggle. To tell them to just trust the unfolding of their life or to see the silver lining in what they have seems insensitive or even wrong. Ive also taught my son to feel lucky that he is fortunate to have things like a home, toys, opportunity, etc., and usually compare his life to those who are less fortunate in order to make the point that he is lucky and that he should be sensitive to other's misfortune. I don't want to teach him that we are any better than they are, but I want him to understand the difference between his luck and others. Although I am not religious (deity), I find myself wanting to pray for those people as I feel like i was simply lucky to be born into a family with opportunity, money, education, etc., whereas they were not. I guess I am a determinist for a lack of a better word. I guess what im asking is what place does sympathy/empathy or even being grateful have in Buddhism when Buddhism teaches that you should accept life for what it is and not to desire more? I can see how that narrative would work for me because i have the things i want, but for people who aren't as fortunate, how do you reconcile that in theory? Even to be motivated to help others, comes down to wanting more for them but Buddhism teaches we shouldn't want more than what has been given to us... Im confused and having trouble reconciling my desire to be grateful, empathetic, help others, etc., when Buddhism says just sit still and accept life for what it is (rich, poor, good, evil, etc.).