You can't compare efforts between marketing and accounting; accounting is non-competitive. I suspect it is an error to try to compare efforts which are dissimilar. The problem set before you is difficult and potentially wicked. On the other hand the only option you can rule out is to do nothing.
I suspect that if I were in your shoes, I'd ask the teams to select and predict their own KPI, and measure them on whether they are in control/able to hit the target they are aiming at.
Ask each department what their goal is, and what their confidence interval is; that is the target, and you can meet regularly to track progress towards that goal. update OP subsequently explained that this is a startup, so I need to modify. Normally the manager has access to the last several years worth of reports, and can calculate the maximum, minimum and median for whatever target they set. The team should be able to explain why their target is different from the median. Since this is a startup, that information isn't available. In many cases reference data is available. Sometimes it is low quality data, but that just affects the confidence intervals. If we were running a mature shop, I would expect the KPI to have a confidence interval of 10%; if we're running a startup, then I might expect a 50% confidence interval. Although I didn't state it earlier, the KPI should be relatively easy to calculate based on available data. You should be able to meet periodically (daily/weekly/monthly as appropriate) and review the current state of the KPI and compare it to the anticipated state. In many cases you should be able to adapt the assumptions & formulas from Earned Value Management. The staff will tell you that their KPI is a special snowflake that has a unique projected value curve. (they should tell you this; if the EVM curve is linear, then they're overpaid). That is fantastic news - that is the opportunity for you to learn their task/business/activity at an appropriate level of detail.
If they can't tell you what their metric is, if they don't have a KPI, then that is a tremendous opportunity; your management will be grateful for any evidence that they're doing work, and you have the opportunity to train them to actually manage their work. That is a problem that is hard, but clear, measurable, relevant and high reward.