You can't edit the date type format.
If you don't want to use the date picker that HTML5 gives you for free, then you could create your own input box with regex restrictions.
<form>
<input type="text" name="input1" placeholder="YYYY-MM" required pattern="[0-9]{4}-[0-9]{2}" />
<input type="submit">
</form>
If you want more strict validation (this one only validates that input is a 4 digit number and a 2 digit number separated by a hyphen), refer to this post
Regex date validation for yyyy-mm-dd
You can play around with the code here:
https://jsfiddle.net/bowenyang/oth9b8o7/