In addition to Sam Nead's answer, which is about how to get started in math research, I want to direct the OP's attention to many lists of open problems in graph theory. For someone with a background in the IMO, who likes problem solving, this is a concrete way to get into research. If you manage to solve one of these open problems, you can publish the solution (there are several MO threads about undergrad math journals that you might find useful, e.g., this one).
Ok, lists of open problems in graph theory:
http://dimacs.rutgers.edu/~hochberg/undopen/graphtheory/graphtheory.html
http://www.openproblemgarden.org/category/graph_theory
Collection of conjectures and open problems in graph theory
Open Problems for Undergraduates
Does there exist a comprehensive compilation of Erdos's open problems?
https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics#Graph_theory
https://mathweb.ucsd.edu/~erdosproblems/
https://dwest.web.illinois.edu/ (two links to lists of open problems)
Spirkl - Open problems for the 2020 Barbados graph theory workshop
Open problems for the Barbados graph theory workshop 2017
Open problems in spectral graph theory: https://arxiv.org/abs/2305.10290 and https://arxiv.org/abs/1907.04349
https://www.cs.upc.edu/~sedthilk/grow/Open_Problems_GROW_2013.pdf
Nguyen - Open problems for the second 2022 Barbados workshop
https://www.quora.com/What-are-some-interesting-unsolved-problems-in-graph-theory-or-topology
Stout - Some open problems and conjectures
Aldous - Some of my favorite open problems
Steinerberger - Some open problems
Gera - Graph theory - Favorite conjectures and open problems - 1
Gera - Graph theory - Favorite conjectures and open problems - 2
Simonovits - Important open problems in extremal graph theory
