In awk $1 references the first field in a record not the first argument like it does in bash. You need to use ARGV for this, check out here for the offical word.
Script:
#!/bin/awk -f
BEGIN{
print "AWK Script"
print ARGV[1]
}
Demo:
$ ./script.awk "Passed in using ARGV"
AWK Script
Passed in using ARGV