How to compile and dump assembly for a c library (string.h)?

For a school project I have to do a large amount of string manipulation in assembly. Since this is a pain to do I was trying to come up with innovative ways to use already programmed string operations. My idea is to compile and dump the assembly from the string.h library in c. Then I would copy paste the dumped assembly into my program. After figuring out the memory location of each function and it's parameters I figure I would essentially be able to call up the function.

To dump the assembly I first wrote a program that included the libraries I wanted:

#include <stdio.h>
#include <string.h>

int main() {

  return 0;
}

Then I compiled and dumped the assembly using

gcc -o lib lib.c
objdump -d  *o

When I looked at the output I noticed that it didn't include any of the assembly for the libraries. My guess is there is either a compiler optimization that doesn't include unused functions, or the library output is hidden when I use objdump:

lib:    file format Mach-O 64-bit x86-64

Disassembly of section __TEXT,__text:
__text:
100000fa0:  55  pushq   %rbp
100000fa1:  48 89 e5    movq    %rsp, %rbp
100000fa4:  31 c0   xorl    %eax, %eax
100000fa6:  c7 45 fc 00 00 00 00    movl    $0, -4(%rbp)
100000fad:  5d  popq    %rbp
100000fae:  c3  retq

_main:
100000fa0:  55  pushq   %rbp
100000fa1:  48 89 e5    movq    %rsp, %rbp
100000fa4:  31 c0   xorl    %eax, %eax
100000fa6:  c7 45 fc 00 00 00 00    movl    $0, -4(%rbp)
100000fad:  5d  popq    %rbp
100000fae:  c3  retq

As a side note I am running OSX Catalina, but I can switch to Ubuntu or a different OS if it would be easier.

How can I go about dumping the asm for the string.h library?