Mom made me a sandwich.
Does this necessarily include the meaning that Mom made the sandwich available to me?
Or does this only mean that Mom made the sandwich, leaving it to context whether or not Mom actually made it available to me?
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"Mom made me a sandwich" means that mom made a sandwich and that the sandwich is for you to eat. It doesn't necessarily mean that she's given you the sandwich yet, but it does imply that she intends to. For example, you could be going on a long trip starting early in the morning. Mom has made sandwiches for everybody, but they're going to stay in her bag until lunch time.
Yes of course it would be available to you. Why would she make it for you and then not let you eat it?
In my opinion, "Mom made me a sandwich" is clear and it does not need the "has". Not that Fresh Learner’s answer is incorrect — it's probably right — but the context on a sentence like "My Mom made me a sandwich" is almost always that she made it for you to eat at that time. It's the "made me" that is key; she didn't make it for someone else, or so that she could eat it.