Getting JavaScript equivalent of DateTime.MinValue

When a string passed into a Date constructor is not in extended ISO format the parsing is completely implementation dependant. If it is in ISO format the parsing is well-defined and it will work exactly the way you want:

var myDate = new Date('0001-01-01T00:00:00Z');
console.log( myDate.getUTCFullYear() );

'1/1/0001' is not the minimum date in JavaScript, -8640000000000000 is the minimum timestamp available in JavaScript, so the minimum date is

new Date(-8640000000000000)

which is Tuesday, April 20th, 271,821 BCE

see here for more details: Minimum and maximum date