In order to understand what a sandwich truly is, we started by looking at various sources that specializes in giving definitions.
1. An item of food consisting of two pieces of bread with a filling between them, eaten as a light meal. (Oxford)
2. A sandwich is a food typically consisting of vegetables, sliced cheese or meat, placed on or between slices of bread, or more generally any dish wherein bread serves as a container or wrapper for another food type. (Wikipedia)
3. Two or more slices of bread or a split roll having a filling in between. (Merriam-Webster)
Simply put, a Sandwich is basically two pieces of bread with something in the middle.
Is a Hamburger a Sandwich?
Once again, we go to the internet to find our answer (and definition).
1. A hamburger (also burger for short) is a sandwich consisting of one or more cooked patties of ground meat, usually beef, placed inside a sliced bread roll or bun. (Wikipedia)
2. (A hamburger is) a sandwich consisting of a patty of hamburger in a split typically round bun. (Merriam-Webster)
So, it is official, a Hamburger is definitely considered a Sandwich.
Oxford (2020) https://www.lexico.com/en/definition/sandwich
Wikipedia (2020) https://en.wikipedia.org/wiki/Sandwich
Merriam-Webster (2020) https://www.merriam-webster.com/dictionary/sandwich
Wikipedia (2020) https://en.wikipedia.org/wiki/Hamburger
Merrium-Webster (2020) https://www.merriam-webster.com/dictionary/hamburger