If your only source was the lyrics. I found a link to what Stookey says it’s about, but what would you guess? Link, if you’re not familiar:
Okay. Never encountered it before, but read the lyrics three times, and listened to the Youtube with my eyes closed. And… I have no good guesses.
I listened for clues about adoption, about sending children to a different country (maybe from Germany), about abortion, about death, about physical birth, about physical death, about pets or other non-human species. I have no good guesses.
I listened to the song. I thought it was about a child being sent away. Maybe a WWII evacuee sent to a home in the country. Maybe sent to boarding school. Maybe to foster care. The child is shy, but has a good singing voice.
Then I googled for the meaning. Nope, my interpretation was totally wrong.
Oh, and it looks like the link goes to an incomplete version of the song. It ends abruptly in the middle of a line.
My contribution: I thought it was about a bird. 
Possibly off to boarding school; possibly a young man who is developmentally challenged.
I got a clue from a Youtube comment, and later read a more thorough explanation. My biggest surprise from the explanation was that what I thought was the major “clue” turned out to not be a clue.
There’s a line about a black room with red carpet, and I thought, “Ahh. A guitar case.” But no, Stookey says that he was checking out the guitar in a black room with red carpet. That’s just massive misdirection on Stookey’s part, since it totally smells like a clue, and is otherwise unimportant. I don’t need misleading anecdotal detail in a song stuffed with metaphor.
I played the hell out of Noel Stookey’s first solo album and his live Real-To-Reel album…live from the Sydney Opera House, and he’s amazed by it (first comment, he whispers that the acoustics are so good you can hear a post-nasal drip).
I always assumed Sebastian was a guitar.
And looking at Stookey’s web site, with its rambling blog, it looks like he does, too.
“hey! this package isn’t for betty; it’s for me! from maine…hey…this must be my guitar! hey, wow!” the mail forgotten, i pick up the large cardboard box and head for the basement studio.
in the unreal, almost vacuum quietness of the black-walled, red-rugged room, i cut the twine holding the package together and gently lift off the top. there are crumpled newspapers on top and, oh my gosh…‘there’s no case here!?’…just the guitar…fortunately it appears as though the box was handled by the carrier with kid gloves.
i lift the casket shaped instrument out of the box. it’s fully strung and there’s a note threaded between the strings that says ‘read before playing’.
“this is sebastian.” reads the note.
https://www.noelpaulstookey.com/tl-1967.html (Italics mine)
I don’t know if digs has just provided the answer, but there were a couple of things in he lyric that I thought pointed in a particular way:
"Sebastian arrived in a cardboard suitcase
Sealed with a kiss from his Mom"
(If I assume that “in” is used poetically). And especially
"When the hand reaches down for the note
The one that his mother wrote
And tied by a string to his neck"
During the second world war, children were evacuated from British cities, carrying what they needed in a suitcase and labelled for ID. See these images, for example (Imperial War Museum article) - in several photos you can see labelled children. In the first image the girl at front of shot (and several other children) has a label around her neck.
They were sent out of the city to the safety of the countryside, to be cared for by strangers they had never met before. That also fits with the tone of the song.
So I dunno, but that was what it made me think of.
j