No, you cannot trade forex without a broker.
In order to place your trades, you need a counter party who is willing to take the opposite side of your trade.
For example, if you want to buy EUR/USD at 1.0200, you need a counterparty who is willing to sell that same pair at that price. This is where a broker comes in.
The DMA or NDD broker on the backend connects you to its LPs/liquidity providers (which are often large banks & other financial institutions in the business of market making) who have access to large liquidity pools, which in this case could be someone (or multiple orders) willing to sell EUR/USD at 1.0200 for the quantity you want to buy.
While a market maker broker could take the opposite side of your trade & give you the fill instantly. In order to protect against market risk, the broker could choose to hedge their exposure if they have a high net exposure in any given currency.
Hypothetically, if you could find someone to take the opposite side of your trade, you could trade without a broker in theory. But you’d struggle to find a trusted counterparty on your own, who could buy & sell whatever you want to trade & whenever you want to take the trade.
The forex market is decentralized and highly liquid, but as a retail trader, who has very low trading volume (meaningless in the overall intraday volume in the FX market), you will not have direct access to the large institutions or banks that make up the bulk of market participants.
Do note that this is just an example. It is obviously more complicated than this.