NFA to DFA: new initial state

Question

Question 4 asks to convert this NFA to a DFA:

The solution is as follows:

Whereas I found this as a solution (excuse the messy layout):

My DFA is identical to the solutions' except the initial state (underlined).

The solutions omitted the 0 state (NFA initial state) and made 1,3 the DFA initial state (mine stays 0).

Can anybody please explain why they removed the 0 state and made 1,3 initial instead?

Edit: the original Q has been answered, but the following NFA to DFA doesn't seem to follow:

The DFA -

I've changed the labels for comprehension:

But shouldn't the new initial state be 1,4 (not in DFA)?

Answer 1

Okay I stumbled on another thread that explains it well: https://math.stackexchange.com/questions/1809453/nfa-to-dfa-removing-unnecessary-states-what-is-new-start-state#:~:text=1%20Answer&text=The%20starting%20state%20of%20the,after%20reading%20the%20word%20%CF%B5.

Basically, the new DFA's initial state is the set of all states the NFA's initial state reached using only epsilon transitions.