3 of 3 yet another fantastic suggestion by my man kev

Java (OpenJDK 8), 67 bytes

a->{int c[]=new int[a.length+1],i=1;for(int u:a)c[i++]=u;return c;}

Try it online!

This was a fun little challenge in Java since Java arrays are static in size, but it seems like this is significantly less challenging in every language that can just slap a zero on for the first- excuse me, zeroth element

Explanation:

int i=1,c[]=new int[a.length+i];    ////Initialize counter and declare new array with length: 1 + input array length
for(int u:a)    //Loop through each element in input array
  c[i++]=u;    //Increment counter after shifting each element up one spot in the output array
return c;    //return new array starting at index 1

Credit:

-3 bytes thanks to Kevin Cruijssen!