1. Good that OP is using 4 simplifications: year 2000-2099, no DST, no leap second, no timezone.  So OP knows of code limitations concerning these.  Various elements of this function break without those givens.

2. Make `static unsigned short days` a `const`.

3. Use a `long` for your epoch in `void epoch_to_date_time(date_time_t* date_time,unsigned int epoch)` as `unsigned` is only guaranteed to range form 0 to at least 65535 which is insufficient here.

4. For various functions consider adding `const`.  The is pros and cons to this, but may be beneficial in your case,:

        // unsigned int date_time_to_epoch(date_time_t* date_time)
        unsigned int date_time_to_epoch(const date_time_t* date_time)

5. There exist algorithmic solutions to the year-day that do not need a table like your  `unsigned short days[4][12]`.  Code then looks more complicated, but it faster.  Please advise if interested.

6.  Most of the magic numbers like 60, 24 are so well known that constant or macro substitution seems superfluous.  But `(365*4+1)` may benefit with something like "DaysPer4Years".