When can an Artificer use ‘Infuse Item’?

While exploring Waterdeep: The Dungeon of the Mad Mage, the party has encountered a few monsters that are resistant to non-magical weapons. The Artificer wants to Infuse the Barbarian’s great sword to make them more effective at tanking. It is about two hours since the party finished a long rest, and the Artificer has not used their Infuse an Item ability in several days.

The somewhat ambiguous text in question from the Artificer class is:

Whenever you finish a long rest, you can touch a non-magical object and imbue it with one of your artificer infusions, turning it into a magic item.

I see two ways to read this:

  • Whenever means ‘at any time after’ you finish a long rest
  • Whenever means ‘immediately after’

Which would be a correct RAW interpretation, and why?

This question goes over a bunch of information about Artificers and their Infusions, but does not cover the ‘when’ answer I seek.

Assuming all other factors have been met to allow this Infusion, When can an Artificer use ‘Infuse an Item’?