AG-Grid – pasting date into agDateStringCellEditor

I want to give ability to paste a date into EDITABLE_DATE_COL_DEF defined below:

// columns.ts
export const EDITABLE_DATE_COL_DEF: AgGrid.ColDef = {
  ...columns.DEFAULT_COL_DEF,
  cellDataType: "dateString",
  cellEditor: "agDateStringCellEditor",
  cellEditorParams: {
    min: columns.formatDate(columns.addDays(columns.dateInTimeZone(new Date()), -180)),
    max: columns.formatDate(columns.dateInTimeZone(new Date())),
  },
  editable: true,
};

The EDITABLE_DATE_COL_DEF is used in the buildGrid in my controller.ts:

function buildGrid($grid: HTMLElement, dataCallbacks: datasource.DatasourceCallbacks, ctrlCallbacks: CtrlCallbacks) {

// (...)

  const colDefs: AgGrid.ColDef[] = [
    { field: "payment_date", ...EDITABLE_DATE_COL_DEF, ...DATE_FILTER_COL_DEF, sortable: true },
    
    // (...) other fields

I can’t find anything relevant in the AG-Grid docs. Is there a way to do this without loosing build-in AG-Grid datepicker?