There was a recent thread on this topic that I think you might find helpful:
https://www.dcurbanmom.com/jforum/posts/list/821708.page
I completely agree that reading is the very best way to pick up vocabulary. Your child doing independent reading is probably best for vocabulary (so that they are seeing the words), but I think you reading to them or using audio books would also give them exposure to new words. They don't have to be classics. You want books that will make your child want to read more. Quantity goes a long way.
All other approaches are a distant second. That being said, learning a foreign language can help strengthen their vocabulary in English.
Paying attention to roots, prefixes, and suffixes can go a long way.
Pay attention to your own vocabulary. Of ypu use a wider vocabulary, your child will pick up wprds from you. Also, when you come across words you don't know, make sure you look them up. It's good to model that behavior for your child.
Games like Scrabble, Bananagrams, Boggle, can get your child thinking about words.
If so inclined, there are multiple gimmicks to help people expand their vocabularies. If one or more is something the kid can enjoy and buy into, go for it! Otherwise, I wouldn't push very hard.
Freerice.com (advertising funded website that donates money to fight world hunger per question answered):
Webster's website has a word a day and some vocabulary quizzes:
https://www.merriam-webster.com/
Hoagies has a lot of links related to words
and vocabulary:
https://www.hoagiesgifted.org/language.htm
You can get paper word-a-day calendars.