In the old days Aristotels argued that object needs a force to keep going in 'space'. Some philosophers, Philoponus and Buridanus (?), later argued that there was a need for some kind of 'impetus'. Did that still imply some kind of active force? Who was the first to suggest that objects only need a force to stop them, but not to keep them moving? Was it Newton or already someone before him?
This depends on which objects you have in mind and who you would call a scientist. There was a broad consensus in the ancient Greek natural philosophy that superlunar objects, like the stars and planets, were moving on their own steam, pardon, divine nature, and uniformly along circles at that. Early mathematical astronomers accepted this conviction to such an extent that when it ostensibly did not match the facts Eudoxus (c. 390–337 BC) came up with extremely clever mathematical construction of homocentric spheres to "save the appearances" this way. To the sublunar matter many natural philosophers ascribed self-motion as well, e.g. Empedoclus, Heraclitus, or the atomists, Leucippus and Democritus, and shortly after Aristotle, Stoics and Epicurus. Even Aristotle himself in addition to "violent motions" maintained by an active force had natural motions to natural places (down for earth and water, up for air and fire), which did not require an acting force and could only be stopped by one, see Rovelli's Aristotle's Physics: a Physicist's Look. It is believed that Newton saw the idea of inertial motion as a modification of Aristotle's natural motions.
On a somewhat more restrictive definition of a scientist, and restricting to the "unnatural" motions of the Earthly objects perhaps the first kind of theory that envisioned self-motion was a modification of Aristotle's theory of the projectile motion, where the "impressed force" was not a prototype of force but a prototype of inertia. It was "impressed" at the time of shooting, and maintained the arrow's flight without the air behind constantly pushing it, as Aristotle contended. The theory is now called impetus theory, and the impetus was a precursor of both notions of momentum (Descartes) and kinetic energy (Leibniz) in 17th century. Here is Franco's Avempace, Projectile Motion, and Impetus Theory on who came up with that:
"While there is almost unanimous agreement about the theory that challenged and eventually supplanted the Aristotelian explanation, there is no such agreement about who first articulated the impetus theory according to which the arrow is kept in motion by a force impressed upon it by the projector. Samuel Sambursky argues that the idea was due to Hipparchus of Nicaea (second century BC), Shlomo Pines ascribes it to Alexander of Aphrodisias (third century AD), Henri Carteron has argued that is to be found first in the pseudo-Aristotelian treatise De Mechanica, McGuire has seen its origins, more generally, in the Stoic influenced John Philoponus (ca. 490-570), whereas Emil Duhem, and, more recently, Richard Sorabji, Michael Wolff, and others trace the idea of impetus to John Philoponus himself".
Hipparchus of Nicea, the father of astronomy, is also the choice of Russo in his Forgotten Revolution, and his analysis of sources is interesting, but he is prone to some passionate exaggerations. Philoponus's mocking suggestion to make the arrow fly by waiving hands behind it was rhetorically effective against the Aristotle's theory, and he was certainly the source of Avicenna, Avempace, and European scholastics like Buridan and Oresme. The latter two developed a somewhat mathematical kinematics that eventually influenced Galileo (how much is controversial), and his idea of inertia, see section V in Skrenes's dissertation Buridan’s Impetus Hypothesis:"Buridan’s impetus is permanent, and in this respect a forerunner of Newtonian inertia... I discuss whether Buridan anticipated Galileo’s law of acceleration."
But even if we restrict to modern scientists, Galileo and Descartes certainly recognized inertial motion before Newton.
Actually, Aristotle argued that all bodies have a natural movement and do not need to be pushed to keep moving. The elements earth and water have a natural movement towards the centre of the cosmos, air and fire have a natural upward movement, and aether (the substance of the heavenly bodies) has a natural circular movement. This is all explained in his treatises “On generation and corruption” and “On the heavens”.