I think this is a problem that most data science teams are facing due to the hype and pressure for ROIs to be generated.
DS teams might work on operational improvements or external customer problems. The same DS team is unlikely to be tasked to do both.
Fairly and factually measuring the impact a team has is not a new problem. Banks have used transfer pricing models to allocate revenue to non-front office teams. This requires a lot of buy-in from higher-ups and it is very sensitive. Management is unlikely to be familiar and comfortable with the notion that a model would calculate the implicit benefit each team is bringing to the table.
Ideas I've seen attempted with various outcomes are:
* If your dashboard leads to hours saved by your internal users, focus on that because this will mean that your DS team's time investment translated into X workhours saved per week or month. Multiply by average salary and you get a cost-saving estimate.
* If your model predicts or calculates something, then it's even easier. It's the same if you are forecasting. It's difficult to measure ROIs on a non-financial investments but it's feasible.
* If your solution does not address an existing modelling need or problem or operational bottleneck and simply modernizes or brings something to the table that was not around before, things are a bit trickier. You need to think about opportunity cost (what could the DS team have been doing instead of this solution) but also what the company's strategic direction is. You also need to address operational risk. If your tool helps minimize the risk, then that's worth something. It's measurable by comparing the data pre and post launch of the tool (maybe a 6 month window of running both is sufficient to compare and contrast).
If you are looking for early stage successes to build the DS team's goodwill - just focus on the first two bullet points. If you already have buy-in, then time is on your side as long as you are productive.
I would also advocate that for conservative companies it's best to ensure that you go to your internal clients and explicitly ask them to nominate projects or problems or issues they need help with. If you can help them with your solutions or data pipelines they will preach for the DS team doing your work for you. Of course, there are a lot of companies where cliques make decisions not just on merit. These companies are going to lose their best people and wither away in time.