die Schwelle
threshold
The lower, horizontal piece of wood or stone in a doorframe that you step over to enter or leave a room.
Pass auf, dass du nicht über die hohe Schwelle stolperst.
Be careful not to trip over the high threshold.

threshold / sill
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threshold
The lower, horizontal piece of wood or stone in a doorframe that you step over to enter or leave a room.
Pass auf, dass du nicht über die hohe Schwelle stolperst.
Be careful not to trip over the high threshold.

The literal meaning refers to doors and buildings. You can recognize the figurative meaning by its combination with abstract terms such as 'Leben' (life), 'Tod' (death), 'Zukunft' (future), or 'Erwachsenwerden' (growing up/adulthood).
Der alte Mann stand an der Schwelle des Todes.
The old man stood on the threshold of death.
When the door threshold is meant, verbs of movement are often used. Typical formulations are 'über die Schwelle treten' (to step over the threshold), 'an der Schwelle stehen' (to stand at/on the threshold), or 'über die Schwelle stolpern' (to trip over the threshold).
Der Gast zögerte, über die Schwelle zu treten.
The guest hesitated to step over the threshold.
The figurative meaning is very often used in the fixed expression 'an der Schwelle zu etwas stehen' (to stand on the threshold of something). The noun after 'zu' is always in the dative.
Die Menschheit steht an der Schwelle zu einem neuen Zeitalter.
Humanity stands on the threshold of a new age.
In connection with trains, tracks, or railway lines, 'Schwelle' (railway sleeper) refers to the crossbeams on which the rails lie. This meaning is very specific to the railway context.
Die Arbeiter verlegen neue Schwellen für die Gleise.
The workers are laying new sleepers for the tracks.
In scientific or technical texts, a 'Schwelle' (threshold) is a limit value from which a reaction begins. You can recognize this meaning from words such as 'Wert' (value), 'Reiz' (stimulus), 'Dosis' (dose), or 'Schmerz' (pain).
Der Lärm überschritt die Schwelle des Erträglichen.
The noise exceeded the threshold of what was bearable.
beginning
'der Anfang' and 'die Schwelle' can both be connected with the beginning of something new. 'der Anfang' directly names the first part or start. In a figurative sense, 'die Schwelle' more often means the boundary just before a new state or a new experience. In a way, you are standing in front of something new and about to enter it. 'Anfang' is more general and more neutral. 'Schwelle' fits when the transition is important, for example 'zur Schwelle eines neuen Lebensabschnitts' (on the threshold of a new phase of life).

Mit dem neuen Job steht Sofia an der Schwelle zu einem anderen Leben.
With her new job, Sofia is on the threshold of a different life.
Am Anfang der Ausbildung lernt man zuerst die wichtigsten Regeln.
At the beginning of the training program, you first learn the most important rules.