preには「事前」と言う意味があります。
質問文を読むとKosugiさんが申し込みを受け入れる側（？）かなと思いました。
We don't know when we'll officially start accepting applications, so we are accepting pre-signups now.
申し込みを正式に受け付け始めるのがいつになるかわからないので、事前申し込みを受け付けています。
この場合、We apologize for the inconvenience.「お手数おかけしてもうしわけありません」と一言加えると良いかもしれないですね。
When something hasn't started yet but registration/application is allowed then all of the "early birds" that want to register can get in on an "Early Registration/application"
In college, for example, class registration begins a couple of months before the following semester begins.
So those students who have a high enough GPA (Grade point Average) can get in on an early registration.
examples
"did you bring your pre-registration documents
with you, you will need these to register".
or
"are you going to the pre-signup session for the course".
or
"are you ready to register for the course".
Pre-sign up, pre-registration is before sign
up or before registration.
Registration is when it actually happens, t
he word pre means previous to, or before
something has happened.
例文：
"did you bring your pre-registration documents
with you, you will need these to register".
事前申し込み書類を持ってきましたか？登録の際に必要ですよ。
"are you going to the pre-signup session for the course".
そのコースの事前申し込みセッションに行きますか？
"are you ready to register for the course".
そのコースの登録の準備はできましたか？
Pre-sign up、pre-registrationは登録前のことです。
Registrationとは実際に「登録する」ことを意味し、preという接頭辞は「〜の前」「〜が起こる前」という意味を表します。
When talking about signing up or applying for something before it starts, we can either use the expressions, "pre-signup," or a, "pre-register," to talk about this. We may also use the term, "early registration," to express that we did the registration process early.
I have had to pre-signup because I will be out of the country on business on the given date.
I have had to pre-register because I will be out of the country on business on the given date.
If a date for signing up or registering has been given but you have been given the option of registering 'before' the given date, this can be called 'pre-signup' or a 'pre-register'. The conjunction 'pre' is a prefiix in this case to indicate that the signup or the registering is being done well before the given date. This does happen often depending on the circumstances of the individual.
So, you may say:
I have had to pre-signup because I will be out of the country on business on the given date.
or
I have had to pre-register because I will be out of the country on business on the given date.
もし申し込み日や登録日が決まっていて、事前に申し込みができる場合は"pre-signup"（事前申し込み）あるいは"pre-register"（事前登録）と呼びます。
接頭辞の"pre"はこの場合、申し込みや登録を事前に行うことを指し示しています。個人の状況に応じて、よくあることですが、以下のように表現できます。
"I have had to pre-signup because I will be out of the country on business on the given date."（申し込み日は仕事で国外にいるため、事前に申し込みをしました。）
"I have had to pre-register because I will be out of the country on business on the given date."（登録日は仕事で国外にいるため、事前に登録をしました。）
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