If I remember correctly,
1st-degree – People you’re directly connected to because you have accepted their invitation to connect, or they have accepted your invitation. You’ll see a 1st degree icon next to their name in search results and on their profile. You can contact them by sending a message on LinkedIn.
2nd-degree – People who are connected to your 1st-degree connections. You’ll see a 2nd degree icon next to their name in search results and on their profile. You can send them an invitation by clicking Connect or contact them through an InMail or an introduction.
3rd-degree – People who are connected to your 2nd-degree connections. You’ll see a 3rd degree icon next to their name in search results and on their profile.
So, my thought process would be if you sent them and invitation and they connect they could become 1st Degree…But I am not 100% Certain…Maybe that is why people recommend introductions to connect