I am about to start playing a game of exalted and i am thinking of making my goal ascending to godhood through i am not sure whether that is possible or not game mechanics wise. Is it possible to become a god as an exalted?
Depends on your definition of godhood, yes for Infernals
If you mean becoming metaphysically like one of the gods of Creation, then no. But there's probably no reason to want to, as gods are generally weaker than high-end Solar Exalts. However, Primordials are much more powerful than gods, and there are mechanics for ascending to Primordialhood of sorts.
The Broken-Winged Crane, starting from page 43, describes Heretical Charms. These are Charms developed by Infernal Exalted (and can only be learned by them, not anybody else, not even Eclipse Solars). The Charm chain starting with the Triumphant Howl of the Devil-Tiger provides a path to becoming the replacements of the Yozis. To clarify, this is an ascension to a level greater than Primordialhood:
Characters on the Heretical transcendence path are not becoming Yozis—they are something new, something much greater.
The path to such ascension has costs and risks, primarily related to all the downsides of learning a bunch of Yozi Charms.
Solars were dealt a less glorious hand
There is a less iconic, but also noteworthy path for Solars too, which also offers an ascension of sorts, and can be found in the Scroll of Errata (the one for the edition number 2½). For example, there is a way for Solars to ascend to Invincible Sun's station (including 'upholding' the Holy effects for everyone), the Should the Sun Not Rise Charm (p. 154).
There is also a series of descriptions of what higher Essence levels mean on page 150, which can be considered a 'soft' mechanical descriptor of an ascension of sorts, culminating in this paragraph:
Charms with an Essence minimum of 10 denote powers beyond those which forged the universe. Not even the Primordials fully understand Essence 10; at this level of effect, the intellects which defined existence find themselves in the position of discovery. What challenges even the Primordials, a Solar may come naturally to grasp and engender: power beyond all reason.
To my knowledge there are no rules published about becoming a literal god, I don't know why you'd want to; as any Exalt, save perhaps the Dragon Bloods, you are already a demigod and start out more divine/powerful than the majority of terrestrial gods and a fair number of the celestial ones as well, and with a couple hundred years under your belt you could rival just about any god your GM cared to name. However, 'impossible' is just a word for things the Solars haven't tried yet, so you do you.
I'll try to be a bit more informative now, There is at least one case that I can think of of a mortal ascending to godhood, I can't think of his name at the moment but he's the Maiden of Serenity's right hand man as I recall... Someone else had to elevate him though, it's not something he accomplished on his own or even intended. He was just some lazy pretty boy that someone took a fancy to.
Things you should consider
Godhood is a job, not a classification of spiritual being. Heaven is literally a bureaucracy, a god becomes more powerful when their domain becomes more important so more celestial resources need to be funneled their way or they otherwise get a promotion.
Gods cannot be Exalted, its written into the Exaltation itself that it will only attach to a human soul. If you became a literal god, a process which will likely be akin to dying, your Exaltation will go find a new host and you will be stuck as a spirit scrabbling and vying for whatever position or power you can with all the rest of them.
As an Celestial Exalt you outrank most gods and are technically entitled to a mansion in Yu-shan, an income of Ambrosia and worship and all the other things most gods can only dream of. However in the current era there are a lot of really dangerous people in the way of actually claiming any of that.
If you are really looking for 'god-like' power (I.E. the ability to manipulate and command certain aspects of creation, create spiritual lairs, perform natural miracles and the like) then you have a few good options:
Eclipse Caste exalts can learn most god charms, becoming capable of doing anything the god they learned it from is, with some caveats.
Create your own charms; this will depend on your GM. Charm creation can be messy and is easily abusable if you don't keep an eye on balance.
Sorcery; admittedly this would require a great deal of house rules but Exalted 3 introduced the ability to use Sorcery much like a craft skill — it's one of my favourite changes 3e made, and if adapted to 2nd edition, could be just what you are looking for.