According to research conducted at the University of Idaho and published in 2014 in the journal Food Protection Trends, there are now consumer guidelines to process garlic (and certain herbs) safely through acidification before adding to oil.
I would read the first link thoroughly to understand the necessary process. To ensure safety, follow the steps precisely. (The second link provides the original scientific paper with detailed data and testing protocols.)
To summarize the procedure:
Peel and chop garlic so that pieces are no more than 1/4" long in any dimension. (Whole cloves or larger pieces are NOT acceptable, since the acid needs to penetrate fully.)
Make a 3% solution of citric acid by combining 1 level Tablespoon of granular citric acid with 2 cups of water. (Note that other acids, lemon juice, vinegars, etc. have NOT been verified and tested for safe home use in this step.)
Combine chopped garlic with a 3% solution of citric acid in a ratio of 1 part garlic to 3 parts citric acid by weight. This is about 2/3 cup of chopped garlic, if you use the amount of acid in step (2).
Let garlic soak in the acid for 24 hours. (This is a minimum to ensure safety; a longer soak may be used, but it could degrade the flavor.)
Drain the acidified garlic well. Combine the acidified garlic with oil, and infuse. A ratio of 1 part garlic to 10 parts oil by weight is recommended, but the ratio can be varied from this to achieve appropriate flavor.
While the procedure recommends removing the garlic once appropriate flavor has been achieved (generally in 1 to 10 days), there is no food safety risk if the garlic is kept in the oil for longer.
As for storage, they write: "Refrigeration of these infused oils is recommended for quality, but not required for safety." And later:
While oils infused with flavors from acidified garlic, basil, oregano,
and rosemary can be safely stored at room temperature, oil flavor
quality is maintained for a longer period of time with refrigerator or
freezer storage. It is also best to protect infused oils from light
by storing them in dark-colored bottles. Make sure the bottles are
clean and food grade. All vegetable oils retain quality better at
cold temperatures and when protected from light.
The scientific paper also notes that the taste and quality of the infused oil produced using this home method was not less than infused commercial oil:
Since panelists were not able to distinguish olive oil infused with
garlic that was acidified with citric acid from the same olive oil
infused with commercially acidified garlic (acidified with phosphoric
acid), the acceptability of citric acid for use in consumer
acidification of garlic and herbs for the production of infused oils
was verified.
Note that acidification is the essential step here and is the only method tested for home use so far to ensure safety for longer storage. The paper specifically notes that there are no approved procedures for pressure canning garlic in oil at home, and non-acidified garlic in oil mixtures must be refrigerated (and used within 2 to 4 days) or frozen.
IMPORTANT DISCLAIMER: Food preservation is not to be taken lightly, particularly in situations that are known risks for botulism. People who are familiar with home canning recipes already know that one should only use approved recipes and procedures that have been thoroughly tested; this procedure is no exception. Botulism risks are generally low, but the consequences of deviating can be severe.
If you are not willing to go through this detailed procedure (or another one approved by a reputable food safety and preservation organization), be sure to store any garlic-infused oils in the refrigerator and use within 2-4 days or freeze.
Best Answer
White wine is most likely acidic enough to be safe. The standard pH level quoted for botulism safety is 4.6; if your jelly measures lower than that (after cooking and canning, not before) then you're good to go. Remember that if you were planning to store all the jars for a while, you'll need to sacrifice one jar to test the pH. Until you have your recipe absolutely, absolutely dialed in (including the brand, variety, and vintage of wine), you'll need to test a jar from each batch.
Seriously, though... consider just buying a real pressure canner. They're not expensive, they're useful for a lot of things other than canning, and they're worth the extra guarantee of safety.