WordPress does NOT provide date picker block by default but have date component inside core. You need to call relevant components for date picker to work. Here’s code from core Date Component
import { DateTimePicker } from '@wordpress/components';
import { getSettings } from '@wordpress/date';
import { withState } from '@wordpress/compose';
const MyDateTimePicker = withState( {
date: new Date(),
} )( ( { date, setState } ) => {
const settings = getSettings();
// To know if the current timezone is a 12 hour time with look for "a" in the time format.
// We also make sure this a is not escaped by a "https://wordpress.stackexchange.com/".
const is12HourTime = /a(?!\\)/i.test(
settings.formats.time
.toLowerCase() // Test only the lower case a
.replace( /\\\\/g, '' ) // Replace "//" with empty strings
.split( '' ).reverse().join( '' ) // Reverse the string and test for "a" not followed by a slash
);
return (
<DateTimePicker
currentDate={ date }
onChange={ ( date ) => setState( { date } ) }
locale={ settings.l10n.locale }
is12Hour={ is12HourTime }
/>
);
} );