The Sage Advice Compendium goes into detail about what happens when you cast a spell without expending a spell slot:
A spell is cast at its lowest possible level, which is the level that appears near the top of its description. Unless you have a special ability that says otherwise or the origin of what allows you to cast a spell without expending a spell slot also allows you specifically to expend a higher-level spell
slot when you cast it; and that the only way to increase the level of a spell is to expend a higher-level spell slot when you cast it.
Sage Advice Compendium version 2.3, page 13:
What level is a spell if you cast it without a spell slot?
Such a spell is cast at its lowest possible level, which is the level
that appears near the top of its description. Unless you have a
special ability that says otherwise, the only way to increase the
level of a spell is to expend a higher-level spell slot when you cast
it. (p 13)
If you have the option to cast a spell at a higher level you have to regard the rules for Casting A Spell at a Higher Level (PHB 201):
When a spellcaster casts a spell using a slot that is of a higher level than the spell, the spell assumes the higher level for that casting.
These origins (in the PHB) of what allows you to cast a spell without expending a spell slot also allows you specifically to expend a higher-level spell slot when you cast it:
Spell Mastery (PHB 115):
If you want to cast either spell at a higher level, you must expend a
spell slot as normal.
Signature Spells (PHB 115):
If you want to cast either spell at a higher level, you must expend a
spell slot as normal.
An example of special abilities that say otherwise is:
Infernal Legacy (PHB 43):
Once you reach 3rd level, you can cast the hellish rebuke spell once per day
as a 2nd-level spell.
That allows you to cast the first-level spell Hellish Rebuke as a second level spell; that is at a higher level than normal, but only at that level.
The wording in the Sage Advice Compendium follows the already in the DMG established wording of:
Boon of Spell Mastery (DMG 232)
Choose one 1st-level sorcerer, warlock, or wizard spell that you can
cast. You can now cast that spell at its lowest level without
expending a spell slot.