Give it to the Magic School Bus. This video from CCP talks about @Mike_Azariah’s efforts (among other topics covered in the video) to furnish free fitted ships to characters younger than 30 days. He gives these ships out in the starter systems, and has done so for years. Operation Magic School Bus is showcased about one minute - twenty into the video.
Just contact Mike. He is doing something very positive for new players, and for that matter, returning player’s using alpha characters younger than 30 days.
Here is his thread in the New Citizens section of the forums. He’s got lots of feed back there. https://forums.eveonline.com/t/operation-magic-school-bus/5352