Java CharSequence iteration
Use Java's built-in functions for things like this. Specifically, Character.isDigit(char c) and String.charAt(int index).

What you have right now is a poor reimplementation that makes any maintenance programmer go "wait, what?".

It sounds mean, but consider what it actually is:

return Character.isDigit(myString.charAt(0));


That one line is all you needed.

To prevent things like this happening in the future, I suggest googling your problem ("java string starts with digit" or "java string starts with number").

You'd have arrived at this question... https://stackoverflow.com/questions/1107798/how-to-check-a-string-starts-with-numeric-number .. which also points you to Character.isDigit. A little bit of google will go a long way in your programming work.

But school said I can't use those methods!

Oh. Okay.

First, store fName.substring(0,1) in a temporary variable. No need to substring forever.
Then, instead of Character.isDigit...

String allowedChars = "0123456789";
String firstChar = fName.substring(0,1);
return allowedChars.contains(firstChar);


After all, String IS CharSequence. You can see this in the documentation of java.lang.String. 

public final class String
extends Object
implements Serializable, Comparable&lt;String&gt;, CharSequence


See, String implements CharSequence.

Bugs

One of the things you need to be aware of is that your function can get a null string or an empty string.

You should check if the string you get is null or empty:

if (fName == null || fName.length == 0){
    return false;
}