You need to customize the column configuration to move the checkbox selection control to the second column in a MUI X DataGridPro tree view,
Here's how to do it:
Solution
import { DataGridPro } from '@mui/x-data-grid-pro';
const columns = [
  {
    field: '__check__',
    headerName: '', 
    width: 50,
  },
  {
    field: 'name',
    headerName: 'Name',
    width: 200,
  },
];
function TreeDataGrid() {
  return (
    <DataGridPro
      rows={rows}
      columns={columns}
      treeData
      getTreeDataPath={(row) => row.hierarchy}
      checkboxSelection
      disableSelectionOnClick
      initialState={{
        columns: {
          columnOrder: ['name', '__check__', /* other columns */], 
        },
      }}
    />
  );
}