There are two honest answers to this question, and you need both.
Two to three months for a first version in production
For a first business tool that your teams use for real work, plan for two to three months. That covers the scoping workshop, the sprints that build the core of the product, and the launch.
We would rather give you this figure than a flattering one. A promise of “a few weeks” usually describes a prototype, not a product your company can rely on.
Two weeks for the first thing you can see
What changes with our way of working is not the date of the launch. It is everything before it.
Each two-week sprint ends with a demo of a version that works. Not slides, not mock-ups: the product, in its current state, doing real things. Between two demos, a test environment stays open, and you can go and look whenever you like.
That means that after two weeks you already know whether we understood you. After a month, your future users can try the main screens. If something is going in the wrong direction, it costs one sprint to correct, not the whole project.
Why a first version, and not everything at once
The first version is not the full dream. It is the smallest product that already removes a real pain: the spreadsheet everyone fights over, the double entry, the phone calls to find out where an order is.
Launching it early has two effects. Your teams start saving time while the rest is being built. And what they say once they use it is worth more than any specification written in advance.
What it means for you
You commit to a quarter, and you check the direction every fortnight. The long wait in the dark, followed by a big reveal, is exactly what this rhythm is designed to avoid.