I was a first time homebuyer in 2016. I purchased this house I live in now, for several tens of thousands below the listing price.
Yes, you should fire your buyer's agent! For house hunting, it is almost always better to not have a buyer's agent.
The "How" would depend on whether you signed an "exclusive buyer's agency" agreement or not, like explained above by BlueHouse. Did you? If so, find it. Does it expire soon? If not, does it have an escape clause for you?
Generally, if you signed a binding contract, then you are bound by it. If it becomes clear that you won't work with the buyer's agent, however, there is no financial incentive for the broker to keep you bound to that agreement. So - maybe, give him some excuse why you can't buy right now at this location that he serves and ask him to let you out of the agreement! Or, you may need to wait out the term of that agreement.
Once you get out of the exclusive agreement, please don't hire a buyer's agent for purchasing hour first house. It is much better to not have one.
All the listings are available on public websites (Zillow/realtor.com/others). You don't need an agent to find them. Once you narrow down the houses you would like from the public info, you should create a ranked list of them and work one by one. Call the top one's seller's agent. Mention to the agent that you are unrepresented. This means double payday for the "seller's agent", so he'll likely work extra hard with you. See if the negotiation works out, if not move down to the next house on the list and repeat.
To make an actual offer, at least in my state, you need to sign a "buyer's agency" agreement. You can't actually do this if you have the "exclusive buyer's agency" agreement from above. Assuming that is a non-issue when you are doing this, ask for a non-exclusive agreement from the seller's agent if he has one. If not, put down the exact address of the house in the "location" field and make sure that the "exclusive" agreement only pertains to this specific house for a reasonable period of time (maybe 6 weeks - enough to close on a deal).
Beware of the fact that when you reach to the seller's agents from the public listings in Zillo/redfin/realtor.com, the seller's agents will try really hard to convince you to hire them as your buyer's agent. I was a first time buyer in 2016 and fell for it once at that time. It was extremely frustrating! A single layer negotiation (seller -> agent -> buyer) is, IMO, useful. You don't want to deal directly with the sellers who are emotionally invested in the house. For the few houses when I tried to engage in a two layer negotiation (seller -> seller's agent -> buyer's agent -> buyer), it was extremely frustrating.
As a first-time homebuyer you may seek the "comfort" of having a buyer's agent. After all, everyone does it and they even promise to work for you. But, in my experience, that "comfort" is a very expensive mirage. You are less likely to have your offer accepted when you have a buyer's agent (i.e. the seller's agent has to split the commission and hence will prioritize the "unrepresented" buyers from who he/she will get double the payday). When your offer is accepted, you will have less leverage to negotiate, and will likely pay a lot more $$ in the end due to this.
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Another useful thing I did was with the pre-approval letter. First time I asked for one, my credit union (DCU, in my case) sent me one with some ridiculous $1M+ number pre-approved for mortgage. I called them back and told them I plan to "lowball" on the houses and don't want any agent or seller to know how much I can borrow. To this, a nice lady in the mortgage department gave me her email address. I would email her every time I need to write a "lowball" offer, and she would email be back a "pre-approval" with the exact number "pre-approved". I wrote 5 offers, and she sent me a different pre-approval letter for each one.
In the end, I purchased an almost-fixer-upper house for what most people in this HCOL location consider a crazy low number (<$300k). I moved into it and working on gradually fixing it up (partially chronicled in this thread:
https://forum.mrmoneymustache.com/real-estate-and-landlording/my-house-needs-some-work-how-would-you-prioritize-differently)