A journey in a temporal graph is a sequence of adjacent and dated edges preserving the increasing order of arrival dates to the consecutive edges. When a journey never visits a vertex twice it is also called a temporal path. Given a pair of source and target vertices, a journey connecting them is foremost if the arrival date at the target vertex is the earliest. Like in the static case, there always exists a foremost journey which is also a temporal path because it is useless to circle around an intermediary vertex. It is therefore equivalent to compute the arrival date of a foremost journey or a foremost temporal path. A non-stop journey is a journey where every pair of consecutive edges must also fulfill a maximum waiting time constraint. Foremost non-stop journeys can achieve strictly earlier arrival date than foremost non-stop temporal paths. We present a linear time algorithm computing the earliest arrival date of such a non-stop journey connecting any two given vertices in a given temporal graph.