I can't offer more than Aksakal does in their answer.
Here are my three suggestions:
1. Time series methods
I've already suggested this in a comment. I think this is a particularly good approach as compared to ML methods because
They are faster to iterate over (you can try many different approaches with time series quickly because they are easy to fit).
They offer estimates of uncertainty (so when you inevitably get the prediction wrong, you can see if the real number was within the prediction interval of the model).
A priori there should be no reason why the number of accounts which provide, for instance, overdraft protection, should influence the accrual of new clients.
For these reasons, I think it is sufficient to simply aggregate the number of new accounts created by month, and then create a time series model via
forecast or similar methods.
2. Linear Regression
Linear regression may be one way forward of time series prove too difficult. Simply aggregate how many accounts were opened last month to predict how many will open this month. You can include features for month of year to capture seasonality, and year to capture trends.
You can count the number of accounts which have overdraft, etc., and use that as a feature. Though I don't think including that information will be relevant, for reasons stated above.
3. Machine Learning
See 2. but instead of doing linear regression, use any ML model you like. If you do this, you lose the ability to make probabilistic statements about the outcome, which you may not care about.
That is really all I can say about your problem. There is no "best" ML approach for these types of things, and you certaintly won't need something like a LSTM NN. Group your data by year-month, count the new accounts, and model as a function of whatever covariates you think are relevant.