The 5e Beast Master ranger's animal companion has a rather significant drawback in some mid- or high-level campaigns. Because animal companions never gain the magical attack feature and due to the lack of a Magic Fang-type spell in 5e, there are particularly deadly fights in which an animal companion may not able to contribute much damage, if any.

Is there any way, as a dedicated Beast Master, to bypass this deficiency and grant a magical attack to your animal companion, even briefly?

At ranger level 7, the animal companion's attacks are treated as magical (as of the 2018 errata)

Per the 2018 PHB errata, the Beast Master ranger's 7th-level feature, Exceptional Training, has been edited to add this benefit:

Beginning at 7th level, on any of your turns when your beast companion doesn’t attack, you can use a bonus action to command the beast to take the Dash, Disengage, or Help action on its turn.

In addition, the beast's attacks now count as magical for the purpose of overcoming resistance and immunity to nonmagical attacks and damage.