可以使用Timer Trigger与Singleton Pattern结合来解决这个问题。首先，在timer trigger的配置中设置一个间隔时间，确保函数会定期运行。接着，在自定义StartUp拓展类的Configure方法中，添加一个单例标记，每次运行函数前首先检查该标记是否存在。若存在，则跳过运行；若不存在，则运行函数，并设置单例标记。以下是C#代码示例：

public class Startup : FunctionsStartup
{
    public override void Configure(IFunctionsHostBuilder builder)
    {
        builder.Services.AddSingleton();

        builder.Services.AddHttpClient();
    }
}

public class Function1
{
    private readonly SingletonService _singletonService;
    private readonly HttpClient _httpClient;

    public Function1(SingletonService singletonService, HttpClient httpClient)
    {
        _singletonService = singletonService;
        _httpClient = httpClient;
    }

    [FunctionName("Function1")]
    public async Task Run([TimerTrigger("0 */5 * * * *")]TimerInfo myTimer, ILogger log)
    {
        log.LogInformation($"C# Timer trigger function executed at: {DateTime.Now}");

        if (_singletonService.InstanceCount == 1)
        {
            log.LogInformation($"Function has already run once on startup.");
            return new OkResult();
        }

        // Function logic
        // ...

        _singletonService.SetInstanceCount(1);
        return new OkResult();
    }
}

public class SingletonService
{
    private int _instanceCount;

    public int InstanceCount => _instanceCount;

    public void SetInstanceCount(int count)
    {
        _instanceCount = count;
    }
}