"Is there an efficient way to provide this information?"
Yes. Players should generally have an index card with monster defenses (at the very least) in their hands around turn 3. Enough attacks will have been made that the defenses will be obvious and it is an excellent way of speeding up combat. If you have a character who routinely makes monster knowledge checks, add sufficient detail to cover her worst possible check, then write additional information on the back. Inform your players when they are allowed to turn over the cards.
This way, there's no interruption of play as the players can read the cards outside their turns. You are not simply printing out the statblock for the players (though that's a quite viable option as well) and you are allowing players to use their knowledge skills to speed up combat.
There are a few classes you can multiclass into to gain skills, such as Bard, Ranger or Rogue.
In addition to that, in the player's handbook there is a feat called "Skilled" which allows you to gain proficiency in any combination of 3 skills or tools.
In Xanathar's Guide to Everything, we have the Prodigy feat which gives a skill proficiency and a few other things, but can only be taken by a Human, Half-Orc, or Half-Elf.
In Tasha's Cauldron of Everything, the feat Skill Expert gives proficiency in a skill and a few other benefits, with no racial prerequisite.
There is also a bard ability in the college of lore that allows you to learn 3 more skills at level 3.
Currently, the downtime rules allow you to gain proficiency in tools but not skills.
In case it isn't clear, you don't have to pick skills from your class skill list when you gain new skills through the "Skilled" feat. You can pick any skill you want.
Best Answer
The short answer is "yes, in downtime."
Player's Handbook
Training in new tool proficiencies is explicitly covered in the Player's Handbook, pg 187, under "Training":
Dungeon Master's Guide
The Dungeon Master's Guide mentions training as a possible reward under the "Marks of Prestige" section (begins on page 228; training is discussed on page 231). No mechanics are given for this; it is entirely the DM's prerogative.
Xanathar's Guide to Everything
Xanathar's introduces more fleshed out rules for downtime activities, one set of which is provided under "Training" on page 134:
Under these rules, the cost would be the same or less, and the time would be significantly less. However, Xanathar's also includes rules for downtime complications that can result; the examples given in the book are all related to something happening to or because of the teacher.