Every answer I saw here so far (July 2023) was wrong. re: Do you "need" a condensate trap - YES, unless your unit specifically comes equipped with an internal trap, you need one. Most package units and virtually ALL split systems require the installation of a dedicated condensate disposal system, including a trap.
2.) A trap is more than a drain. I quote here typical condensate trap information from a typical well known package unit manufacturer's install documentation.
"Do not operate unit without a drain trap. The Condensate drain is on the negative pressure side of the blower; thererfore, air being pulled through the condensate line will prevent positive drainage without a proper trap" The bolds are from the manufacturer.
Once you install the trap you must PRIME it to get it started. Do not depend on the condensate from the unit to prime it. Every minute your unit runs without a trap, or with an un-primed trap it is sucking warm outside air, dirt, bugs, mold, etc. right through the trap and right into your conditioned air space, because that entire circuit is "ON THE NEGATIVE PRESSURE SIDE OF THE BLOWER".
Most traps need about 3" lift to work correctly and allow for static pressure fluctuations.
Besides the dirt/mold/warm air/fiasco, your current situation is draining condensate onto the chassis of your unit. This will lead to corrosion, because condensate is water, and can also be slightly acidic.
Finally, did you not notice that your installer left your unit on the delivery skid when he installed it?