My question: is there any way to tell Perl NOT to do that, and to stop at the first (next) statement in the body of the code?

So you're asking for a means to have the debugger skip over some of the program? It doesn't make much sense to have a debugger that skips over pieces of code. You'll have to add a condition to the code.

#!/usr/bin/perl
INIT {
    return if $ENV{DEBUG_SKIP_INIT};
    print "here INIT\n";
}
print "here main\n";
[download]

Then launch the debugger using

DEBUG_SKIP_INIT=1 perl -d
[download]

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