You are confused. String.toCharArray() does not remove or "skip" spaces. It delivers exactly the sequence of characters as they are in the String.
The most likely problem is that the (expected) leading space is not in that string (first_string) at all. You can check by temporarily adding this line:
System.err.println("first_string is '" + first_string + "'");
and looking at the output. Or you could use a debugger to set a breakpoint and examine the value of first_string directly.
Hints for debugging:
If your program misbehaves in a way that you can't explain / understand, then question your assumptions:
Read / reread the javadocs to check that the library methods you are using actually do what you think / remember they do.
Check that the relevant variables have the values that you think they should have.
And ... learn how to use your IDE's debugger, 'cos you will save lots of time if you can use a debugger effectively.
first_string?