Not sure if there are additional requirements for e-residents, but for the standard end of the year accounting requirements you don't need to have cash. There's a general net worth requirement, which can pretty easily be filled with company owned equipment like a laptop and smartphone.
"If the net assets are less than half of the share capital or less than the minimum capital requirement of EUR2,500 regarding private limited liability companies and EUR250,000 regarding public limited liability companies, the shareholders must decide on:
(1) The implementation of measures as a result of which the net assets would form at least half of the share capital and minimum capital requirement Or
(2) Dissolution, merger, division, transformation of the company Or
(3) Submission of a bankruptcy petition"
