
der Eingang
entrance
An area through which one can enter a building, room, or site.
Der Eingang des Museums befindet sich auf der rechten Seite.
The entrance to the museum is on the right-hand side.
entrance / receipt
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entrance
An area through which one can enter a building, room, or site.
Der Eingang des Museums befindet sich auf der rechten Seite.
The entrance to the museum is on the right-hand side.

receipt
The arrival or receipt of something, especially mail, payments, messages, or data.
Wir bestätigen den Eingang Ihrer Bewerbung per E-Mail.
We will confirm receipt of your application by email.

opening
The beginning or start of a work, for example a text, a piece of music, or a speech.
Schon der Eingang des Romans fesselte die Leser.
Even the opening of the novel captivated the readers.
The word 'Eingang' (entrance / receipt) is made up of the prefix 'ein-' and the noun 'Gang' (from 'gehen' (to go)). So it literally describes a 'way in' to a building or area.
Bitte benutzen Sie den Eingang auf der Rückseite des Gebäudes.
Please use the entrance at the back of the building.
You can recognize the meaning of 'Eingang' (entrance / receipt) from the context. If it is about a place (house, museum), it means access or entrance. If it is about mail or data (letter, email, payment), it means arrival or receipt. With works (book, music), it means the beginning.
Der Eingang zum Park ist bis 20 Uhr geöffnet.
The entrance to the park is open until 8 p.m.
To describe a location, use 'am Eingang' (at the entrance). To express movement toward it, say 'zum Eingang' (to the entrance).
Wir treffen uns in zehn Minuten am Haupteingang.
We'll meet in ten minutes at the main entrance.
In the meaning 'Eintreffen' (arrival/receipt), 'Eingang' (receipt) is used mainly in formal written language, in the office, or in business correspondence.
Nach Eingang der Zahlung versenden wir die Ware umgehend.
After receipt of payment, we will ship the goods immediately.
Common combinations are 'den Eingang bestätigen' (to confirm receipt), 'nach Eingang' (after receipt), and 'bei Eingang' (upon receipt). A very common compound is 'der Posteingang' (inbox).
Bitte bestätigen Sie den Eingang dieser E-Mail kurz.
Please briefly confirm receipt of this email.
beginning
Anfang and Eingang can both refer to the first part of a speech or text. Anfang is neutral and generally understandable in this use. Eingang sounds literary or technical and is more suitable when the opening part of a work is deliberately emphasized.

Der kunstvolle Eingang der Rede greift ein bekanntes Zitat auf.
The speech's artful opening refers to a well-known quotation.
Der Anfang der Rede greift ein bekanntes Zitat auf.
The beginning of the speech refers to a well-known quotation.