As someone who obsesses about optimizing processes that support people and organizations, onboarding and transitioning are two things I think about for at least an hour a day. Lately, I was thinking specifically about when the ideal time is to start creating transition documents.
From observation and experience, it seems to be the case that starting to create your transition report after you give notice is way too late in the game (unless the role is a very simple one). If the notice was given 2 weeks (read 10 business days) before you leave, that actually doesn’t leave a lot of time for you to get everything documented.
Also: when your heart is elsewhere, it becomes very easy to half-ass everything at your current work. That includes your transition report. For this reason, starting to create your transition report when you make the decision to leave your current role is still not good enough. Although you may have much more time compared to the previous scenario depending on how much time elapses between the moment you decide to leave your role and when you officially give notice, the half-assing problem doesn’t go away. The moment your heart checks out, it becomes very difficult to put in the level of care you used to put into your work (back when you really cared about what you did at your current role). I’ve seen this with my predecessors, and I am guilty of this too.
So when is the best time to start the transition report? You start creating your transition report on the day you start in your new role. The secret is to not think of a transition report as something that becomes relevant only when you leave your role. A transition report is there to help YOU as well as your successor. The report exists so that you can do cognitive offloading - you don't need to constantly have everything in your head because it's also in the report. You can refer back to it if you forget something. It is your safety net and long-term investment.
You know all the notes you take when you start a new role and hike up that steep learning curve? (I hope you have those!) Do yourself a favor and combine all of them into a way that is presentable. Then you're doing two valuable things at once - you're setting your future self and your successor up for success :)
On "role creep"
You may have heard of the term "scope creep" in management:
"Scope creep (also called requirement creep, or kitchen sink syndrome) in project management refers to changes, continuous or uncontrolled growth in a project’s scope, at any point after the project begins. This can occur when the scope of a project is not properly defined, documented, or controlled."
(From Wikipedia "Scope Creep";  Lewis, James (2002). Fundamentals of Project Management (Second ed.). AMACOM. pp. 29, 63. ISBN 0-8144-7132-3.)
This "creeping" can also happen in roles too.
When a role "is not properly defined, documented, or controlled," role creep is bound to happen.
One example is the role of supervisor or manager. In some unfortunate cases, some supervisors role creep / micromanage due to the fear of "letting go" of the responsibilities that should be handled by their direct reports. Have you experienced your manager stepping on your toes all the time? The failure to delegate is something that I have struggled to tackle, and I have not found a solution for it (it probably needs to be dealt with on a case by case basis anyways).
If you join an organization that is attempting to expand rapidly, your role will likely experience role creep. You'll probably be asked to wear say 3 hats at the time of hire, but when an organization is forced to "do more with less," one day you'll notice that you have 20 hats instead of the original 3. Some people find this enjoyable but others will find this exhausting.
When the organization is large and stable, role creep may be the key to get you a raise or to get you promoted. If you voluntarily wear more hats and prove to the employer that you can take more things on (or new things on), that may open doors for future opportunities. Let me tell you my relationship with role creep: Whenever I wanted to wear a new hat and my supervisor said "no" to it because it was out of my "scope"... that hat was - consistently - the hat I ended up wearing in my next job. So if you're faced with a situation where you want to wear a hat but get shut down, it may still be worth doing research around that hat (even if you can't wear it immediately). You never know when you'll get a chance to wear it. It could be right around the corner...
I'm Candice and I doodle with the intensity of the doomguy.