You can use an Autotransformer to accomplish this for a lower price than a step-up transformer, but it has its limits.
The following information only applies to the unit I'm linking below. Other autotransformers may work differently and have their own code requirements. You must use circuit breakers that are suitable for backfeed operation.
First, feed your 120v inverter into your main panel on one of the legs, preferrably L1, with a suitable sized, backfed, single pole breaker for the inverter's output. This must be clearly identified as your "MAIN" breaker.
Second, you would install a 2 pole 25 amp breaker, preferably next to the main breaker. This is going to be feeding to the autotransformer.
Third, feed four wires, Green, White, Black and Red (GND, N, L1, L2) through a conduit or seal-tight tubing to the autotransformer. You must use at least a #10awg wire for this.
Fourth, Connect GND to the terminal marked with the ground symbol in the autotransformer. Connect the black wire to L1, Neutral to N, and Red to L2
Fifth, check all wiring for short circuits, as a precaution.
Finally, power on the inverter first, with no other loads in the panel powered. After the inverter is on, turn on the breaker to the autotransformer. You should hear a subtle but audible hum coming from the transformer. Using a volt-meter, verify L1-N has 120v, L2-N has 120v, and L1-L2 has 240v. If you are seeing close to these voltages, then you may proceed to turn on the breakers to your utilization equipment (loads).
With this system, you are limited to 5000va (watts) on L2, therefore I recommend planning a maximum system capability of 10,000 watts to prevent overloads of the transformer and subsequent tripping of the breaker, shutting down half of the panel (and all loads connected to L2).
Here is the transformer I am referring to:
https://store.currentconnected.com/product/solaredge-seauto-5kva-autotransformer/
Please do note that I am linking to a product that I sell on my webstore and make a profit from. I am very familiar with this product, hence why I am willing to give advice for it so freely. With that being said, if you do purchase this product from us, we are more than happy to guide you through every step of the installation process, outlined above.
EDIT: I forgot I was going to link a video I made as well!