No, do not wait! Three months is not too soon - begin applying now. To directly answer your question, there is no such thing as your application being "lost in their system." Every application is associated directly with the position to which it is submitted. So, you should apply to any and all positions of interest - you are not capped at one application after which your application is "lost in the system."
Finding a job is a full-time job itself, and it can take weeks just to start hearing back from companies. Here is the worst-case scenario if you apply now, along with some common scenarios that are more likely.
You apply now, and the company reaches out soon. You are honest and discuss timelines. A good Recruiter would bring it up, but you should ask if they don't and alert them to your situation. If your timeline is unrealistic, they will let you know. You should use that opportunity to let them know you are interested in their company in the future, and ask the Recruiter for any insights into future openings, other types of positions that might be a good fit for your background, and any career advice they might have.
RESULT: You have now gained additional insight into the process, a connection at the company you are interested in, and even the possibility that the Recruiter reaches back out to you for their next opening!
- Many hiring managers emphasize finding the right fit over small logistical challenges like an extended timeline. The value of hiring the right person (and opportunity cost of hiring the wrong person) far exceeds any value from hiring someone else a couple of weeks sooner.
- Many positions have flexible start dates and can work around the candidate's timeline.
- The hiring process can often take weeks or even months to go through.
- They could have another of the same position opening coming in the future and decide to pull from the original recruiting package instead of re-posting, thus neglecting to apply now could cause you to miss that future opportunity.
RESULT: Applying now has no negative impact, but it could be the positive difference-maker in landing a job there.