Mathematica online: How to evaluate initialization cells (only)

FrontEndToken solution won't work because it is not implemented yet.

You could filter InitializationCell from Cells[], then scan them with SelectionMove+SelectionEvaluate. Unfortunately it seems you can select CellContents but not Cell so SelectionEvaluate won't work...

Assuming you don't need them to generate output you could do:

ToExpression @* First @* NotebookRead /@ Select[CurrentValue[#,InitializationCell]&] @ Cells[];