Miracles and Providence in Christian theism
As you are asking about Christianity, I think the first place to start is by noting that Christianity is explicitly opposed to Deism, the belief that God exists and created the world, but does not intervene or even really interact with it now. The god of Deism is unknown and unknowable, but the Christian God, right from the beginning of humanity, has communicated, related with, and intervened in the lives of people and the world he created. Though he is not part of the created universe, he has never been far from it, and it exists only because he sustains it.
So there is a sense in which God's interventions in this world are natural: natural to how God is in himself, a relational being who loves his creation, and natural from our perspective, as the whole history of humanity has been one in which God is active.
Second, though we often think of there being a strong dichotomy between the natural and the supernatural, Christian theology does not accept that. Instead Christianity teaches the doctrine of Providence: God's continuous sustaining of the universe. Providence is ultimately one act of God, even though it takes different forms at different times. So see the Westminster Confession of Faith on providence:
5.1: God the great Creator of all things does uphold, direct, dispose, and govern all creatures, actions, and things, from the greatest even to the least, by His most wise and holy providence, according to His infallible foreknowledge, and the free and immutable counsel of His own will, to the praise of the glory of His wisdom, power, justice, goodness, and mercy.
5.2: Although, in relation to the foreknowledge and decree of God, the first Cause, all things come to pass immutably, and infallibly; yet, by the same providence, He orders them to fall out, according to the nature of second causes, either necessarily, freely, or contingently.
5.3: God, in His ordinary providence, makes use of means, yet is free to work without, above, and against them, at His pleasure.
In paragraph 2 we read that God is the first cause, by which all things come to pass, but that God ordains that what happens happens through secondary causes, according to their nature. As it is the nature for fire to be hot, ice to be cold, and heavy masses to pull light masses towards them, so these secondary causes are used to work out the providence of God. By itself this might seem to prohibit miracles which go against the nature of things, but paragraph three says that God is free to use these means, or to work without, above, or against them as he wishes. The miracles of God are the times when he decided to use unusual secondary causes, but even then they were not times when every law of nature was suspended. For example, in the miracle of Jesus calming the storm, however it came to pass, gravity still remained in place, and the waters and atmosphere still followed their currents and convections. So rather than thinking of natural and supernatural (or unnatural), it's probably more helpful to think of ordinary and extraordinary.
In this Christian view of God I would say it does imply believing in miracles, because miracles are ultimately only distinguished from the ordinary by the free pleasure of God to act as he wills. For the Providence of God to not have capacity for extraordinary secondary causes would mean that God is beholden to a will more powerful than his own.
The limits of science and the necessity of extraordinary creation
Christians believe God has created a consistent and ordered universe, one in which the enterprise of science can be productive. Although every single physical phenomena is direct result of God's providence, his ordinary providence is so reliable that we can study the universe and construct models of the physical world with incredible detail. So in the rare times when he deems to use non-ordinary means, our scientific enterprise is not able to account for what he does.
Consider the simplest possible miracle, the creation of something from nothing, even as simple as a single photon. If God decided to do this, it would be impossible for science to account for it, because of the law of the conservation of mass/energy. Indeed, it wouldn't even be possible for us to observe it happening, at that scale we can't even compare observation to scientific model. And were we to detect the existence of the photon, all we could say is that it had been travelling in a straight line at constant speed. If we traced its path we might identify a supposed source, or we might have to conclude that its source is beyond our observational reach. But there's no capacity in our observational abilities or our models for it to simply come into existence.
For a similar but larger scale miracle, consider the water turning into wine. At that scale natural human observation can contradict scientific modelling. But scientific study could not be reconciled with naive sort of observation of the wedding attendants. We could analyse the wine and determine what type of grapes it was made from, how old the wine is, perhaps where it was made. We wouldn't detect that it had come into existence just minutes before. The miracle is not that Jesus turned water into minutes old wine, but into quality wine that had been aged for years in barrels in a cellar somewhere. Science could tell us how old the wine was, and that would in a very real sense be the truth.
Christian theology teaches that only God is eternal and self-existent, everything else that is, exists and is contingent on him. We can produce wonderful models with science, but we can't ultimately account for existence. Christians believe God created the universe, and this necessitates a miracle, one which is beyond science. Whether God created through the big bang, or in six days out of nothing, the world that he created is one in which there is matter and energy and laws in how they interact. In an expanding universe the only stable configuration is a singularity, so however God created the universe, when we looked back to model the past, we couldn't see the creation of everything, but only expansion from a singularity. But as I said, we can't account for existence, and science doesn't try. So when there is a fundamental distinction between creator and creation, as Christianity teaches, I believe this does imply believing in miracles, at least the original miracle of the universe.