The Signature Spells feature says:
When you reach 20th level, you gain mastery over two powerful spells and can cast them with little effort. Choose two 3rd-level wizard spells in your spellbook as your signature spells. You always have these spells prepared, they don’t count against the number of spells you have prepared, and you can cast each of them once at 3rd level without expending a spell slot. When you do so, you can’t do so again until you finish a short or long rest.
If you want to cast either spell at a higher level, you must expend a spell slot as normal.
You gain the benefits of leveling up as soon as you level up, unless the DM house-rules otherwise. The feature requires you to choose two 3rd-level spells in your spellbook as your signature spells; if you are unable to do so, you simply don't get the benefit of the feature. This choice can not be made at some later point.
That said, this is a very unlikely situation; the only way it would be possible is if you picked only 1st- or 2nd-level spells when you gained your 5th and 6th wizard levels, and continued picking only non-3rd-level spells as you continued leveling up. (Or, I suppose, if your spellbook was somehow lost/destroyed after your 6th wizard level and you never chose a 3rd-level spell after that.)
Obviously, this would be a terrible idea, as you'd get nothing from the capstone feature. At the same time that the player goes up to level 20, they get to add 2 spells to their spellbook as always; if they've somehow managed to accidentally never take 3rd-level spells for some reason (which really is highly unlikely without doing so intentionally), they can do so when they go up to 20th level.