Great question! My response is based on experience...
There's companies you must assume their limited contact info is for a reason.
There's companies like startups, local or midsize firms that are more welcomed even if they lacked the knowledge of value in more contact info in their sites.. What i have done in the past is Google a relevant employee and try a variation of their name and email.. Sometimes it works sometimes it doesn't.
If you can't get a name then to that general inbox address yourself with as a higher rank title as possible without lying or becoming liable, state that you are requesting a contact number or address so that you can stop by and introduce yourself and maybe drop off some goodies (I have dropped off sweets, donuts, & coffee) aks that if they prefer to give you a call and schedule a visit to please do so by a certain date.

This approach very often works for me.

Never, even in person, do you introduce yourself for the purpose of gaining something from others and immediately ask for a favor or their business. Build a relationship even if is a thin one... Then when you know your offering is either welcomed or needed do you pitch or ask...
This might limited the amount of pitches you do online but the quality will increase. :)