If you can get geocoordinates instead of just a state you could use this:
https://hexdocs.pm/tz_world/TzWorld.html#timezone_at/2

Ontario from your example lies in 3 time zones. I don’t think you can do a mapping like that which would be generic enough.

If you can provide a UN LOCODE then you can resolve the applicable timezone, or timezones, by calling Cldr.Timezone.fetch/1.

locode is quite useful in lots of applications so maybe that’s a good canonical approach for your requirements too?

Example

iex> Cldr.Timezone.fetch("usnyc")
{:ok, ["America/New_York", "US/Eastern"]}

iex> Cldr.Timezone.fetch("ausyd")
{:ok,
 ["Australia/Sydney", "Australia/ACT", "Australia/Canberra", "Australia/NSW"]}

iex> Cldr.Timezone.fetch("uslax")
{:ok, ["America/Los_Angeles", "US/Pacific", "US/Pacific-New", "PST8PDT"]}

iex> Cldr.Timezone.fetch("nope")
:error

And if locode isn’t workable for you, you could map your coding to locodes. The data to help with that can be retrieved with:

iex> Cldr.Timezone.timezones() |> Enum.filter(fn {k, _v} -> String.starts_with?(k, "us") end)
[
  {"usmnm", ["America/Menominee"]},
  {"ustel", ["America/Indiana/Tell_City"]},
  {"usind",
   ["America/Indianapolis", "America/Fort_Wayne",
    "America/Indiana/Indianapolis", "US/East-Indiana"]},
  {"usden",
   ["America/Denver", "America/Shiprock", "Navajo", "US/Mountain", "MST7MDT"]},
  {"ushnl", ["Pacific/Honolulu", "US/Hawaii", "Pacific/Johnston", "HST"]},
  {"uswsq", ["America/Indiana/Petersburg"]},
  ...
]