There are many publishers that are open to short story submissions from young and emerging writers. Here are a few examples:
Electric Literature - This publisher is dedicated to promoting and publishing emerging writers, and accepts short story submissions through its weekly fiction magazine, Recommended Reading.
Glimmer Train - This publisher is known for publishing literary fiction, and has a monthly short story award for new and emerging writers.
The Kenyon Review - This literary magazine has a long history of publishing new and emerging writers, and has a monthly short story contest for writers under the age of 30.
The Masters Review - This online literary magazine publishes short fiction by new and emerging writers, and has a monthly short story contest for writers under the age of 35.
The New Yorker - This magazine has a long history of publishing short fiction by some of the most well-known and respected authors in the field, and accepts submissions from new and emerging writers.
Ploughshares - This literary magazine publishes poetry, fiction, and nonfiction, and has a monthly short story contest for new and emerging writers.
Tin House - This literary magazine publishes poetry, fiction, and nonfiction, and has a monthly short story contest for new and emerging writers.
It's worth noting that many publishers accept un-agented submissions, and many have open submission periods.It's always recommended to check the publisher's website and submission guidelines before submitting your work.